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<h1 class="quarto-secondary-nav-title"><span class="chapter-number">47</span> <span class="chapter-title">Surface Area</span></h1>
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<h2 id="toc-title">Table of contents</h2>
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<li><a href="#surfaces-of-revolution" id="toc-surfaces-of-revolution" class="nav-link active" data-scroll-target="#surfaces-of-revolution"> <span class="header-section-number">47.1</span> Surfaces of revolution</a>
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<li><a href="#the-first-theorem-of-pappus" id="toc-the-first-theorem-of-pappus" class="nav-link" data-scroll-target="#the-first-theorem-of-pappus"> <span class="header-section-number">47.2</span> The first Theorem of Pappus</a></li>
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<li><a href="#questions" id="toc-questions" class="nav-link" data-scroll-target="#questions"> <span class="header-section-number">47.3</span> Questions</a></li>
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<h1 class="title d-none d-lg-block"><span class="chapter-number">47</span> <span class="chapter-title">Surface Area</span></h1>
|
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</header>
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<p>This section uses these add-on packages:</p>
|
||
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">CalculusWithJulia</span></span>
|
||
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">Plots</span></span>
|
||
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">SymPy</span></span>
|
||
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">QuadGK</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
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<hr>
|
||
<section id="surfaces-of-revolution" class="level2" data-number="47.1">
|
||
<h2 data-number="47.1" class="anchored" data-anchor-id="surfaces-of-revolution"><span class="header-section-number">47.1</span> Surfaces of revolution</h2>
|
||
<div class="quarto-figure quarto-figure-center">
|
||
<figure class="figure">
|
||
<p><img src="../integrals/figures/gehry-hendrix.jpg" class="img-fluid figure-img"></p>
|
||
<p></p><figcaption class="figure-caption">The exterior of the Jimi Hendrix Museum in Seattle has the signature style of its architect Frank Gehry. The surface is comprised of patches. A general method to find the amount of material to cover the surface - the surface area - might be to add up the area of <em>each</em> of the patches. However, in this section we will see for surfaces of revolution, there is an easier way. (Photo credit to <a href="http://firepanjewellery.com/">firepanjewellery</a>.)</figcaption><p></p>
|
||
</figure>
|
||
</div>
|
||
<blockquote class="blockquote">
|
||
<p>The surface area generated by rotating the graph of <span class="math inline">\(f(x)\)</span> between <span class="math inline">\(a\)</span> and <span class="math inline">\(b\)</span> about the <span class="math inline">\(x\)</span>-axis is given by the integral</p>
|
||
<p><span class="math display">\[
|
||
\int_a^b 2\pi f(x) \cdot \sqrt{1 + f'(x)^2} dx.
|
||
\]</span></p>
|
||
<p>If the curve is parameterized by <span class="math inline">\((g(t), f(t))\)</span> between <span class="math inline">\(a\)</span> and <span class="math inline">\(b\)</span> then the surface area is</p>
|
||
<p><span class="math display">\[
|
||
\int_a^b 2\pi f(t) \cdot \sqrt{g'(t)^2 + f'(t)^2} dx.
|
||
\]</span></p>
|
||
<p>These formulas do not add in the surface area of either of the ends.</p>
|
||
</blockquote>
|
||
<div class="cell" data-hold="true" data-execution_count="5">
|
||
<div class="cell-output cell-output-display" data-execution_count="6">
|
||
<p><img src="surface_area_files/figure-html/cell-6-output-1.svg" class="img-fluid"></p>
|
||
</div>
|
||
</div>
|
||
<p>The above figure shows a cone (the line <span class="math inline">\(y=x\)</span>) presented as a surface of revolution about the <span class="math inline">\(x\)</span>-axis.</p>
|
||
<p>To see why this formula is as it is, we look at the parameterized case, the first one being a special instance with <span class="math inline">\(g(t) =t\)</span>.</p>
|
||
<p>Let a partition of <span class="math inline">\([a,b]\)</span> be given by <span class="math inline">\(a = t_0 < t_1 < t_2 < \cdots < t_n =b\)</span>. This breaks the curve into a collection of line segments. Consider the line segment connecting <span class="math inline">\((g(t_{i-1}), f(t_{i-1}))\)</span> to <span class="math inline">\((g(t_i), f(t_i))\)</span>. Rotating this around the <span class="math inline">\(x\)</span> axis will generate something approximating a disc, but in reality will be the frustum of a cone. What will be the surface area?</p>
|
||
<p>Consider a right-circular cone parameterized by an angle <span class="math inline">\(\theta\)</span> and the largest radius <span class="math inline">\(r\)</span> (so that the height satisfies <span class="math inline">\(r/h=\tan(\theta)\)</span>). If this cone were made of paper, cut up a side, and layed out flat, it would form a sector of a circle, whose area would be <span class="math inline">\(R\gamma\)</span> where <span class="math inline">\(R\)</span> is the radius of the circle (also the side length of our cone), and <span class="math inline">\(\gamma\)</span> an angle that we can figure out from <span class="math inline">\(r\)</span> and <span class="math inline">\(\theta\)</span>. To do this, we note that the arc length of the circle’s edge is <span class="math inline">\(R\gamma\)</span> and also the circumference of the bottom of the cone so <span class="math inline">\(R\gamma = 2\pi r\)</span>. With all this, we can solve to get <span class="math inline">\(A = \pi r^2/\sin(\theta)\)</span>. But we have a frustum of a cone with radii <span class="math inline">\(r_0\)</span> and <span class="math inline">\(r_1\)</span>, so the surface area is a difference: <span class="math inline">\(A = \pi (r_1^2 - r_0^2) /\sin(\theta)\)</span>.</p>
|
||
<p>Relating this to our values in terms of <span class="math inline">\(f\)</span> and <span class="math inline">\(g\)</span>, we have <span class="math inline">\(r_1=f(t_i)\)</span>, <span class="math inline">\(r_0 = f(t_{i-1})\)</span>, and <span class="math inline">\(\sin(\theta) = \Delta f / \sqrt{(\Delta g)^2 + (\Delta f)^2}\)</span>, where <span class="math inline">\(\Delta f = f(t_i) - f(t_{i-1})\)</span> and similarly for <span class="math inline">\(\Delta g\)</span>.</p>
|
||
<p>Putting this altogether we get that the surface area generarated by rotating the line segment around the <span class="math inline">\(x\)</span> axis is</p>
|
||
<p><span class="math display">\[
|
||
\text{sa}_i = \pi (f(t_i)^2 - f(t_{i-1})^2) \cdot \sqrt{(\Delta g)^2 + (\Delta f)^2} / \Delta f =
|
||
\pi (f(t_i) + f(t_{i-1})) \cdot \sqrt{(\Delta g)^2 + (\Delta f)^2}.
|
||
\]</span></p>
|
||
<p>(This is <span class="math inline">\(2 \pi\)</span> times the average radius times the slant height.)</p>
|
||
<p>As was done in the derivation of the formula for arc length, these pieces are multiplied both top and bottom by <span class="math inline">\(\Delta t = t_{i} - t_{i-1}\)</span>. Carrying the bottom inside the square root and noting that by the mean value theorem <span class="math inline">\(\Delta g/\Delta t = g(\xi)\)</span> and <span class="math inline">\(\Delta f/\Delta t = f(\psi)\)</span> for some <span class="math inline">\(\xi\)</span> and <span class="math inline">\(\psi\)</span> in <span class="math inline">\([t_{i-1}, t_i]\)</span>, this becomes:</p>
|
||
<p><span class="math display">\[
|
||
\text{sa}_i = \pi (f(t_i) + f(t_{i-1})) \cdot \sqrt{(g'(\xi))^2 + (f'(\psi))^2} \cdot (t_i - t_{i-1}).
|
||
\]</span></p>
|
||
<p>Adding these up, <span class="math inline">\(\text{sa}_1 + \text{sa}_2 + \cdots + \text{sa}_n\)</span>, we get a Riemann sum approximation to the integral</p>
|
||
<p><span class="math display">\[
|
||
\text{SA} = \int_a^b 2\pi f(t) \sqrt{g'(t)^2 + f'(t)^2} dt.
|
||
\]</span></p>
|
||
<p>If we assume integrability of the integrand, then as our partition size goes to zero, this approximate surface area converges to the value given by the limit. (As with arc length, this needs a technical adjustment to the Riemann integral theorem as here we are evaluating the integrand function at four points (<span class="math inline">\(t_i\)</span>, <span class="math inline">\(t_{i-1}\)</span>, <span class="math inline">\(\xi\)</span> and <span class="math inline">\(\psi\)</span>) and not just at some <span class="math inline">\(c_i\)</span>.</p>
|
||
<div class="cell" data-cache="true" data-hold="true" data-execution_count="6">
|
||
<div class="cell-output cell-output-display" data-execution_count="7">
|
||
<div class="d-flex justify-content-center"> <figure class="figure"> <img src="data:image/gif;base64,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" class="card-img-top figure-img" alt="A Figure">
|
||
<figcaption class="figure-caption"><div class="markdown"><p>Surface of revolution of \(f(x) = 2 - x^2\) about the \(y\) axis. The lines segments are the images of rotating the secant line connecting \((1/2, f(1/2))\) and \((3/4, f(3/4))\). These trace out the frustum of a cone which approximates the corresponding surface area of the surface of revolution. In the limit, this approximation becomes exact and a formula for the surface area of surfaces of revolution can be used to compute the value.</p>
|
||
</div> </figcaption>
|
||
</figure>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<section id="examples" class="level4">
|
||
<h4 class="anchored" data-anchor-id="examples">Examples</h4>
|
||
<p>Lets see that the surface area of an open cone follows from this formula, even though we just saw how to get this value.</p>
|
||
<p>A cone be be envisioned as rotating the function <span class="math inline">\(f(x) = x\tan(\theta)\)</span> between <span class="math inline">\(0\)</span> and <span class="math inline">\(h\)</span> around the <span class="math inline">\(x\)</span> axis. This integral yields the surface area:</p>
|
||
<p><span class="math display">\[
|
||
\begin{align*}
|
||
\int_0^h 2\pi f(x) \sqrt{1 + f'(x)^2}dx
|
||
&= \int_0^h 2\pi x \tan(\theta) \sqrt{1 + \tan(\theta)^2}dx \\
|
||
&= (2\pi\tan(\theta)\sqrt{1 + \tan(\theta)^2} x^2/2 \big|_0^h \\
|
||
&= \pi \tan(\theta) \sec(\theta) h^2 \\
|
||
&= \pi r^2 / \sin(\theta).
|
||
\end{align*}
|
||
\]</span></p>
|
||
<p>(There are many ways to express this, we used <span class="math inline">\(r\)</span> and <span class="math inline">\(\theta\)</span> to match the work above. If the cone is parameterized by a height <span class="math inline">\(h\)</span> and radius <span class="math inline">\(r\)</span>, then the surface area of the sides is <span class="math inline">\(\pi r\sqrt{h^2 + r^2}\)</span>. If the base is included, there is an additional <span class="math inline">\(\pi r^2\)</span> term.)</p>
|
||
<section id="example" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example">Example</h5>
|
||
<p>Let the graph of <span class="math inline">\(f(x) = x^2\)</span> from <span class="math inline">\(x=0\)</span> to <span class="math inline">\(x=1\)</span> be rotated around the <span class="math inline">\(x\)</span> axis. What is the resulting surface area generated?</p>
|
||
<p><span class="math display">\[
|
||
\text{SA} = \int_a^b 2\pi f(x) \sqrt{1 + f'(x)^2}dx = \int_0^1 2\pi x^2 \sqrt{1 + (2x)^2} dx.
|
||
\]</span></p>
|
||
<p>This integral is done by a trig substitution, but gets involved. We let <code>SymPy</code> do it:</p>
|
||
<div class="cell" data-execution_count="7">
|
||
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="pp">@syms</span> x</span>
|
||
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>F <span class="op">=</span> <span class="fu">integrate</span>(<span class="fl">2</span> <span class="op">*</span> PI <span class="op">*</span> x<span class="op">^</span><span class="fl">2</span> <span class="op">*</span> <span class="fu">sqrt</span>(<span class="fl">1</span> <span class="op">+</span> (<span class="fl">2</span>x)<span class="op">^</span><span class="fl">2</span>), x)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="8">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
2 \pi \left(\frac{x^{5}}{\sqrt{4 x^{2} + 1}} + \frac{3 x^{3}}{8 \sqrt{4 x^{2} + 1}} + \frac{x}{32 \sqrt{4 x^{2} + 1}} - \frac{\operatorname{asinh}{\left(2 x \right)}}{64}\right)
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>We show <code>F</code>, only to demonstrate that indeed the integral is a bit involved. The actual surface area follows from a <em>definite</em> integral, which we get through the fundamental theorem of calculus:</p>
|
||
<div class="cell" data-execution_count="8">
|
||
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">F</span>(<span class="fl">1</span>) <span class="op">-</span> <span class="fu">F</span>(<span class="fl">0</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="9">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
2 \pi \left(- \frac{\operatorname{asinh}{\left(2 \right)}}{64} + \frac{9 \sqrt{5}}{32}\right)
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
</section>
|
||
<section id="plotting-surfaces-of-revolution" class="level3" data-number="47.1.1">
|
||
<h3 data-number="47.1.1" class="anchored" data-anchor-id="plotting-surfaces-of-revolution"><span class="header-section-number">47.1.1</span> Plotting surfaces of revolution</h3>
|
||
<p>The commands to plot a surface of revolution will be described more clearly later; for now we present them as simply a pattern to be followed in case plots are desired. Suppose the curve in the <span class="math inline">\(x-y\)</span> plane is given parametrically by <span class="math inline">\((g(u), f(u))\)</span> for <span class="math inline">\(a \leq u \leq b\)</span>.</p>
|
||
<p>To be concrete, we parameterize the circle centered at <span class="math inline">\((6,0)\)</span> with radius <span class="math inline">\(2\)</span> by:</p>
|
||
<div class="cell" data-execution_count="9">
|
||
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="fu">g</span>(u) <span class="op">=</span> <span class="fl">6</span> <span class="op">+</span> <span class="fl">2</span><span class="fu">sin</span>(u)</span>
|
||
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="fu">f</span>(u) <span class="op">=</span> <span class="fl">2</span><span class="fu">cos</span>(u)</span>
|
||
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>a, b <span class="op">=</span> <span class="fl">0</span>, <span class="fl">2</span>pi</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="10">
|
||
<pre><code>(0, 6.283185307179586)</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>The plot of this curve is:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="10">
|
||
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>us <span class="op">=</span> <span class="fu">range</span>(a, b, length<span class="op">=</span><span class="fl">100</span>)</span>
|
||
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(<span class="fu">g</span>.(us), <span class="fu">f</span>.(us), xlims<span class="op">=</span>(<span class="op">-</span><span class="fl">0.5</span>, <span class="fl">9</span>), aspect_ratio<span class="op">=:</span>equal, legend<span class="op">=</span><span class="cn">false</span>)</span>
|
||
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="fu">plot!</span>([<span class="fl">0</span>,<span class="fl">0</span>],[<span class="op">-</span><span class="fl">3</span>,<span class="fl">3</span>], color<span class="op">=:</span>red, linewidth<span class="op">=</span><span class="fl">5</span>) <span class="co"># y axis emphasis</span></span>
|
||
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="fu">plot!</span>([<span class="fl">3</span>,<span class="fl">9</span>], [<span class="fl">0</span>,<span class="fl">0</span>], color<span class="op">=:</span>green, linewidth<span class="op">=</span><span class="fl">5</span>) <span class="co"># x axis emphasis</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="11">
|
||
<p><img src="surface_area_files/figure-html/cell-11-output-1.svg" class="img-fluid"></p>
|
||
</div>
|
||
</div>
|
||
<p>Though parametric plots have a convenience constructor, <code>plot(g, f, a, b)</code>, we constructed the points with <code>Julia</code>’s broadcasting notation, as we will need to do for a surface of revolution. The <code>xlims</code> are adjusted to show the <span class="math inline">\(y\)</span> axis, which is emphasized with a layered line. The line is drawn by specifying two points, <span class="math inline">\((x_0, y_0)\)</span> and <span class="math inline">\((x_1, y_1)\)</span> in the form <code>[x0,x1]</code> and <code>[y0,y1]</code>.</p>
|
||
<p>Now, to rotate this about the <span class="math inline">\(y\)</span> axis, creating a surface plot, we have the following pattern:</p>
|
||
<div class="cell" data-execution_count="11">
|
||
<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="fu">S</span>(u,v) <span class="op">=</span> [<span class="fu">g</span>(u)<span class="fu">*cos</span>(v), <span class="fu">g</span>(u)<span class="fu">*sin</span>(v), <span class="fu">f</span>(u)]</span>
|
||
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>us <span class="op">=</span> <span class="fu">range</span>(a, b, length<span class="op">=</span><span class="fl">100</span>)</span>
|
||
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>vs <span class="op">=</span> <span class="fu">range</span>(<span class="fl">0</span>, <span class="fl">2</span>pi, length<span class="op">=</span><span class="fl">100</span>)</span>
|
||
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>ws <span class="op">=</span> <span class="fu">unzip</span>(<span class="fu">S</span>.(us, vs<span class="op">'</span>)) <span class="co"># reorganize data</span></span>
|
||
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a><span class="fu">surface</span>(ws<span class="op">...</span>, zlims<span class="op">=</span>(<span class="op">-</span><span class="fl">6</span>,<span class="fl">6</span>), legend<span class="op">=</span><span class="cn">false</span>)</span>
|
||
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a><span class="fu">plot!</span>([<span class="fl">0</span>,<span class="fl">0</span>], [<span class="fl">0</span>,<span class="fl">0</span>], [<span class="op">-</span><span class="fl">3</span>,<span class="fl">3</span>], color<span class="op">=:</span>red, linewidth<span class="op">=</span><span class="fl">5</span>) <span class="co"># y axis emphasis</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="12">
|
||
<p><img src="surface_area_files/figure-html/cell-12-output-1.svg" class="img-fluid"></p>
|
||
</div>
|
||
</div>
|
||
<p>The <code>unzip</code> function is not part of base <code>Julia</code>, rather part of <code>CalculusWithJulia</code>. This function rearranges data into a form consumable by the plotting methods like <code>surface</code>. In this case, the result of <code>S.(us,vs')</code> is a grid (matrix) of points, the result of <code>unzip</code> is three grids of values, one for the <span class="math inline">\(x\)</span> values, one for the <span class="math inline">\(y\)</span> values, and one for the <span class="math inline">\(z\)</span> values. A manual adjustment to the <code>zlims</code> is used, as <code>aspect_ratio</code> does not have an effect with the <code>plotly()</code> backend and errors on 3d graphics with <code>pyplot()</code>.</p>
|
||
<p>To rotate this about the <span class="math inline">\(x\)</span> axis, we have this pattern:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="12">
|
||
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="fu">S</span>(u,v) <span class="op">=</span> [<span class="fu">g</span>(u), <span class="fu">f</span>(u)<span class="fu">*cos</span>(v), <span class="fu">f</span>(u)<span class="fu">*sin</span>(v)]</span>
|
||
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>us <span class="op">=</span> <span class="fu">range</span>(a, b, length<span class="op">=</span><span class="fl">100</span>)</span>
|
||
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>vs <span class="op">=</span> <span class="fu">range</span>(<span class="fl">0</span>, <span class="fl">2</span>pi, length<span class="op">=</span><span class="fl">100</span>)</span>
|
||
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>ws <span class="op">=</span> <span class="fu">unzip</span>(<span class="fu">S</span>.(us,vs<span class="op">'</span>))</span>
|
||
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a><span class="fu">surface</span>(ws<span class="op">...</span>, legend<span class="op">=</span><span class="cn">false</span>)</span>
|
||
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a><span class="fu">plot!</span>([<span class="fl">3</span>,<span class="fl">9</span>], [<span class="fl">0</span>,<span class="fl">0</span>],[<span class="fl">0</span>,<span class="fl">0</span>], color<span class="op">=:</span>green, linewidth<span class="op">=</span><span class="fl">5</span>) <span class="co"># x axis emphasis</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="13">
|
||
<p><img src="surface_area_files/figure-html/cell-13-output-1.svg" class="img-fluid"></p>
|
||
</div>
|
||
</div>
|
||
<p>The above pattern covers the case of rotating the graph of a function <span class="math inline">\(f(x)\)</span> of <span class="math inline">\(a,b\)</span> by taking <span class="math inline">\(g(t)=t\)</span>.</p>
|
||
<section id="example-1" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example-1">Example</h5>
|
||
<p>Rotate the graph of <span class="math inline">\(x^x\)</span> from <span class="math inline">\(0\)</span> to <span class="math inline">\(3/2\)</span> around the <span class="math inline">\(x\)</span> axis. What is the surface area generated?</p>
|
||
<p>We work numerically for this one, as no antiderivative is forthcoming. Recall, the accompanying <code>CalculusWithJulia</code> package defines <code>f'</code> to return the automatic derivative through the <code>ForwardDiff</code> package.</p>
|
||
<div class="cell" data-hold="true" data-execution_count="13">
|
||
<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="fu">f</span>(x) <span class="op">=</span> x<span class="op">^</span>x</span>
|
||
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>a, b <span class="op">=</span> <span class="fl">0</span>, <span class="fl">3</span><span class="op">/</span><span class="fl">2</span></span>
|
||
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a>val, _ <span class="op">=</span> <span class="fu">quadgk</span>(x <span class="op">-></span> <span class="fl">2</span>pi <span class="op">*</span> <span class="fu">f</span>(x) <span class="op">*</span> <span class="fu">sqrt</span>(<span class="fl">1</span> <span class="op">+</span> f<span class="op">'</span>(x)<span class="op">^</span><span class="fl">2</span>), a, b)</span>
|
||
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a>val</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="14">
|
||
<pre><code>14.934256764843937</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>(The function is not defined at <span class="math inline">\(x=0\)</span> mathematically, but is on the computer to be <span class="math inline">\(1\)</span>, the limiting value. Even were this not the case, the <code>quadgk</code> function doesn’t evaluate the function at the points <code>a</code> and <code>b</code> that are specified.)</p>
|
||
<div class="cell" data-hold="true" data-execution_count="14">
|
||
<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">g</span>(u) <span class="op">=</span> u</span>
|
||
<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a><span class="fu">f</span>(u) <span class="op">=</span> u<span class="op">^</span>u</span>
|
||
<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a><span class="fu">S</span>(u,v) <span class="op">=</span> [<span class="fu">g</span>(u)<span class="fu">*cos</span>(v), <span class="fu">g</span>(u)<span class="fu">*sin</span>(v), <span class="fu">f</span>(u)]</span>
|
||
<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a>us <span class="op">=</span> <span class="fu">range</span>(<span class="fl">0</span>, <span class="fl">3</span><span class="op">/</span><span class="fl">2</span>, length<span class="op">=</span><span class="fl">100</span>)</span>
|
||
<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a>vs <span class="op">=</span> <span class="fu">range</span>(<span class="fl">0</span>, <span class="cn">pi</span>, length<span class="op">=</span><span class="fl">100</span>) <span class="co"># not 2pi (to see inside)</span></span>
|
||
<span id="cb11-6"><a href="#cb11-6" aria-hidden="true" tabindex="-1"></a>ws <span class="op">=</span> <span class="fu">unzip</span>(<span class="fu">S</span>.(us,vs<span class="op">'</span>))</span>
|
||
<span id="cb11-7"><a href="#cb11-7" aria-hidden="true" tabindex="-1"></a><span class="fu">surface</span>(ws<span class="op">...</span>, alpha<span class="op">=</span><span class="fl">0.75</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="15">
|
||
<p><img src="surface_area_files/figure-html/cell-15-output-1.svg" class="img-fluid"></p>
|
||
</div>
|
||
</div>
|
||
<p>We compare this answer to that of the frustum of a cone with radii <span class="math inline">\(1\)</span> and <span class="math inline">\((3/2)^2\)</span>, formed by rotating the line segment connecting <span class="math inline">\((0,f(0))\)</span> with <span class="math inline">\((3/2,f(3/2))\)</span>. From looking at the graph of the surface, these values should be comparable. The surface area of the cone part is <span class="math inline">\(\pi (r_1^2 + r_0^2) / \sin(\theta) = \pi (r_1 + r_0) \cdot \sqrt{(\Delta h)^2 + (r_1-r_0)^2}\)</span>.</p>
|
||
<div class="cell" data-hold="true" data-execution_count="15">
|
||
<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="fu">f</span>(x) <span class="op">=</span> x<span class="op">^</span>x</span>
|
||
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>r0, r1 <span class="op">=</span> <span class="fu">f</span>(<span class="fl">0</span>), <span class="fu">f</span>(<span class="fl">3</span><span class="op">/</span><span class="fl">2</span>)</span>
|
||
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a><span class="cn">pi</span> <span class="op">*</span> (r1 <span class="op">+</span> r0) <span class="op">*</span> <span class="fu">sqrt</span>((<span class="fl">3</span><span class="op">/</span><span class="fl">2</span>)<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> (r1<span class="op">-</span>r0)<span class="op">^</span><span class="fl">2</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="16">
|
||
<pre><code>15.310680925915081</code></pre>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="example-2" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example-2">Example</h5>
|
||
<p>What is the surface area generated by Gabriel’s Horn, the solid formed by rotating <span class="math inline">\(1/x\)</span> for <span class="math inline">\(x \geq 1\)</span> around the <span class="math inline">\(x\)</span> axis?</p>
|
||
<p><span class="math display">\[
|
||
\text{SA} = \int_a^b 2\pi f(x) \sqrt{1 + f'(x)^2}dx =
|
||
\lim_{M \rightarrow \infty} \int_1^M 2\pi \frac{1}{x} \sqrt{1 + (-1/x^2)^2} dx.
|
||
\]</span></p>
|
||
<p>We do this with <code>SymPy</code>:</p>
|
||
<div class="cell" data-execution_count="16">
|
||
<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="pp">@syms</span> M</span>
|
||
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a>ex <span class="op">=</span> <span class="fu">integrate</span>(<span class="fl">2</span>PI <span class="op">*</span> (<span class="fl">1</span><span class="op">/</span>x) <span class="op">*</span> <span class="fu">sqrt</span>(<span class="fl">1</span> <span class="op">+</span> (<span class="op">-</span><span class="fl">1</span><span class="op">/</span>x)<span class="op">^</span><span class="fl">2</span>), (x, <span class="fl">1</span>, M))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="17">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
2 \pi \left(- \frac{M}{\sqrt{M^{2} + 1}} + \operatorname{asinh}{\left(M \right)} - \frac{1}{M \sqrt{M^{2} + 1}}\right) - 2 \pi \left(- \sqrt{2} + \log{\left(1 + \sqrt{2} \right)}\right)
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>The limit as <span class="math inline">\(M\)</span> gets large is of interest. The only term that might get out of hand is <code>asinh(M)</code>. We check its limit:</p>
|
||
<div class="cell" data-execution_count="17">
|
||
<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="fu">limit</span>(<span class="fu">asinh</span>(M), M <span class="op">=></span> oo)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="18">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
\infty
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>So indeed it does. There is nothing to balance this out, so the integral will be infinite, as this shows:</p>
|
||
<div class="cell" data-execution_count="18">
|
||
<div class="sourceCode cell-code" id="cb16"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="fu">limit</span>(ex, M <span class="op">=></span> oo)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="19">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
\infty
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>This figure would have infinite surface, were it possible to actually construct an infinitely long solid. (But it has been shown to have <em>finite</em> volume.)</p>
|
||
</section>
|
||
<section id="example-3" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example-3">Example</h5>
|
||
<p>The curve described parametrically by <span class="math inline">\(g(t) = 2(1 + \cos(t))\cos(t)\)</span> and <span class="math inline">\(f(t) = 2(1 + \cos(t))\sin(t)\)</span> from <span class="math inline">\(0\)</span> to <span class="math inline">\(\pi\)</span> is rotated about the <span class="math inline">\(x\)</span> axis. Find the resulting surface area.</p>
|
||
<p>The graph shows half a heart, the resulting area will resemble an apple.</p>
|
||
<div class="cell" data-hold="true" data-execution_count="19">
|
||
<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="fu">g</span>(t) <span class="op">=</span> <span class="fl">2</span>(<span class="fl">1</span> <span class="op">+</span> <span class="fu">cos</span>(t)) <span class="op">*</span> <span class="fu">cos</span>(t)</span>
|
||
<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a><span class="fu">f</span>(t) <span class="op">=</span> <span class="fl">2</span>(<span class="fl">1</span> <span class="op">+</span> <span class="fu">cos</span>(t)) <span class="op">*</span> <span class="fu">sin</span>(t)</span>
|
||
<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(g, f, <span class="fl">0</span>, <span class="fl">1</span>pi)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="20">
|
||
<p><img src="surface_area_files/figure-html/cell-20-output-1.svg" class="img-fluid"></p>
|
||
</div>
|
||
</div>
|
||
<p>The integrand simplifies to <span class="math inline">\(8\sqrt{2}\pi \sin(t) (1 + \cos(t))^{3/2}\)</span>. This lends itself to <span class="math inline">\(u\)</span>-substitution with <span class="math inline">\(u=\cos(t)\)</span>.</p>
|
||
<p><span class="math display">\[
|
||
\begin{align*}
|
||
\int_0^\pi 8\sqrt{2}\pi \sin(t) (1 + \cos(t))^{3/2}
|
||
&= 8\sqrt{2}\pi \int_1^{-1} (1 + u)^{3/2} (-1) du\\
|
||
&= 8\sqrt{2}\pi (2/5) (1+u)^{5/2} \big|_{-1}^1\\
|
||
&= 8\sqrt{2}\pi (2/5) 2^{5/2} = \frac{2^7 \pi}{5}.
|
||
\end{align*}
|
||
\]</span></p>
|
||
</section>
|
||
</section>
|
||
</section>
|
||
<section id="the-first-theorem-of-pappus" class="level2" data-number="47.2">
|
||
<h2 data-number="47.2" class="anchored" data-anchor-id="the-first-theorem-of-pappus"><span class="header-section-number">47.2</span> The first Theorem of Pappus</h2>
|
||
<p>The <a href="http://tinyurl.com/le3lvb9">first</a> theorem of Pappus provides a simpler means to compute the surface area if the distance the centroid is from the axis (<span class="math inline">\(\rho\)</span>) and the arc length of the curve (<span class="math inline">\(L\)</span>) are both known. In that case, the surface area satisfies:</p>
|
||
<p><span class="math display">\[
|
||
\text{SA} = 2 \pi \rho L
|
||
\]</span></p>
|
||
<p>That is, the surface area is simply the circumference of the circle traced out by the centroid of the curve times the length of the curve - the distances rotated are collapsed to that of just the centroid.</p>
|
||
<section id="example-4" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example-4">Example</h5>
|
||
<p>The surface area of of an open cone can be computed, as the arc length is <span class="math inline">\(\sqrt{h^2 + r^2}\)</span> and the centroid of the line is a distance <span class="math inline">\(r/2\)</span> from the axis. This gives SA<span class="math inline">\(=2\pi (r/2) \sqrt{h^2 + r^2} = \pi r \sqrt{h^2 + r^2}\)</span>.</p>
|
||
</section>
|
||
<section id="example-5" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example-5">Example</h5>
|
||
<p>We can get the surface area of a torus from this formula.</p>
|
||
<p>The torus is found by rotating the curve <span class="math inline">\((x-b)^2 + y^2 = a^2\)</span> about the <span class="math inline">\(y\)</span> axis. The centroid is <span class="math inline">\(b\)</span>, the arc length <span class="math inline">\(2\pi a\)</span>, so the surface area is <span class="math inline">\(2\pi (b) (2\pi a) = 4\pi^2 a b\)</span>.</p>
|
||
<p>A torus with <span class="math inline">\(a=2\)</span> and <span class="math inline">\(b=6\)</span></p>
|
||
<div class="cell" data-hold="true" data-execution_count="20">
|
||
<div class="cell-output cell-output-display" data-execution_count="21">
|
||
<p><img src="surface_area_files/figure-html/cell-21-output-1.svg" class="img-fluid"></p>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="example-6" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example-6">Example</h5>
|
||
<p>The surface area of sphere will be SA<span class="math inline">\(=2\pi \rho (\pi r) = 2 \pi^2 r \cdot \rho\)</span>. What is <span class="math inline">\(\rho\)</span>? The centroid of an arc formula can be derived in a manner similar to that of the centroid of a region. The formulas are:</p>
|
||
<p><span class="math display">\[
|
||
\begin{align}
|
||
\text{cm}_x &= \frac{1}{L} \int_a^b g(t) \sqrt{g'(t)^2 + f'(t)^2} dt\\
|
||
\text{cm}_y &= \frac{1}{L} \int_a^b f(t) \sqrt{g'(t)^2 + f'(t)^2} dt.
|
||
\end{align}
|
||
\]</span></p>
|
||
<p>Here, <span class="math inline">\(L\)</span> is the arc length of the curve.</p>
|
||
<p>For the sphere parameterized by <span class="math inline">\(g(t) = r \cos(t)\)</span>, <span class="math inline">\(f(t) = r\sin(t)\)</span>, we get that these become</p>
|
||
<p><span class="math display">\[
|
||
\text{cm}_x = \frac{1}{L}\int_0^\pi r\cos(t) \sqrt{r^2(\sin(t)^2 + \cos(t)^2)} dt = \frac{1}{L}r^2 \int_0^\pi \cos(t) = 0.
|
||
\]</span></p>
|
||
<p><span class="math display">\[
|
||
\text{cm}_y = \frac{1}{L}\int_0^\pi r\sin(t) \sqrt{r^2(\sin(t)^2 + \cos(t)^2)} dt = \frac{1}{L}r^2 \int_0^\pi \sin(t) = \frac{1}{\pi r} r^2 \cdot 2 = \frac{2r}{\pi}.
|
||
\]</span></p>
|
||
<p>Combining this, we see that the surface area of a sphere is <span class="math inline">\(2 \pi^2 r (2r/\pi) = 4\pi r^2\)</span>, by Pappus’ Theorem.</p>
|
||
</section>
|
||
</section>
|
||
<section id="questions" class="level2" data-number="47.3">
|
||
<h2 data-number="47.3" class="anchored" data-anchor-id="questions"><span class="header-section-number">47.3</span> Questions</h2>
|
||
<section id="questions-1" class="level5">
|
||
<h5 class="anchored" data-anchor-id="questions-1">Questions</h5>
|
||
<p>The graph of <span class="math inline">\(f(x) = \sin(x)\)</span> from <span class="math inline">\(0\)</span> to <span class="math inline">\(\pi\)</span> is rotated around the <span class="math inline">\(x\)</span> axis. After a <span class="math inline">\(u\)</span>-substitution, what integral would give the surface area generated?</p>
|
||
<div class="cell" data-hold="true" data-execution_count="21">
|
||
<div class="cell-output cell-output-display" data-execution_count="22">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="12222821778415219289" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_12222821778415219289">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_12222821778415219289_1">
|
||
<input class="form-check-input" type="radio" name="radio_12222821778415219289" id="radio_12222821778415219289_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
\(-\int_1^{_1} 2\pi u^2 \sqrt{1 + u} du\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_12222821778415219289_2">
|
||
<input class="form-check-input" type="radio" name="radio_12222821778415219289" id="radio_12222821778415219289_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
\(-\int_1^{_1} 2\pi u \sqrt{1 + u^2} du\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_12222821778415219289_3">
|
||
<input class="form-check-input" type="radio" name="radio_12222821778415219289" id="radio_12222821778415219289_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
\(-\int_1^{-1} 2\pi \sqrt{1 + u^2} du\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="12222821778415219289_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_12222821778415219289"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 3;
|
||
var msgBox = document.getElementById('12222821778415219289_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_12222821778415219289")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_12222821778415219289")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
})});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
<p>Though the integral can be computed by hand, give a numeric value.</p>
|
||
<div class="cell" data-hold="true" data-execution_count="22">
|
||
<div class="cell-output cell-output-display" data-execution_count="23">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="5732042234612353131" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_5732042234612353131">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="5732042234612353131" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="5732042234612353131_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("5732042234612353131").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 14.4235994484141) <= 0.001);
|
||
var msgBox = document.getElementById('5732042234612353131_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_5732042234612353131")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_5732042234612353131")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="questions-2" class="level5">
|
||
<h5 class="anchored" data-anchor-id="questions-2">Questions</h5>
|
||
<p>The graph of <span class="math inline">\(f(x) = \sqrt{x}\)</span> from <span class="math inline">\(0\)</span> to <span class="math inline">\(4\)</span> is rotated around the <span class="math inline">\(x\)</span> axis. Numerically find the surface area generated?</p>
|
||
<div class="cell" data-hold="true" data-execution_count="23">
|
||
<div class="cell-output cell-output-display" data-execution_count="24">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="12278343873028348651" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_12278343873028348651">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="12278343873028348651" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="12278343873028348651_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("12278343873028348651").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 36.176903197411335) <= 0.001);
|
||
var msgBox = document.getElementById('12278343873028348651_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_12278343873028348651")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_12278343873028348651")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="questions-3" class="level5">
|
||
<h5 class="anchored" data-anchor-id="questions-3">Questions</h5>
|
||
<p>Find the surface area generated by revolving the graph of the function <span class="math inline">\(f(x) = x^3/9\)</span> from <span class="math inline">\(x=0\)</span> to <span class="math inline">\(x=2\)</span> around the <span class="math inline">\(x\)</span> axis. This can be done by hand or numerically.</p>
|
||
<div class="cell" data-hold="true" data-execution_count="24">
|
||
<div class="cell-output cell-output-display" data-execution_count="25">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="13366711452522980756" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_13366711452522980756">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="13366711452522980756" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="13366711452522980756_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("13366711452522980756").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 3.80093925989871) <= 0.001);
|
||
var msgBox = document.getElementById('13366711452522980756_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_13366711452522980756")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_13366711452522980756")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="questions-4" class="level5">
|
||
<h5 class="anchored" data-anchor-id="questions-4">Questions</h5>
|
||
<p>(From Stewart.) If a loaf of bread is in the form of a sphere of radius <span class="math inline">\(1\)</span>, the amount of crust for a slice depends on the width, but not where in the loaf it is sliced.</p>
|
||
<p>That is this integral with <span class="math inline">\(f(x) = \sqrt{1 - x^2}\)</span> and <span class="math inline">\(u, u+h\)</span> in <span class="math inline">\([-1,1]\)</span> does not depend on <span class="math inline">\(u\)</span>:</p>
|
||
<p><span class="math display">\[
|
||
A = \int_u^{u+h} 2\pi f(x) \sqrt{1 + f'(x)^2} dx.
|
||
\]</span></p>
|
||
<p>If we let <span class="math inline">\(f(x) = y\)</span> then <span class="math inline">\(f'(x) = x/y\)</span>. With this, what does the integral above come down to after cancellations:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="25">
|
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<p>Find the surface area of the dome of sphere generated by rotating the the curve generated by <span class="math inline">\(g(t) = \cos(t)\)</span> and <span class="math inline">\(f(t) = \sin(t)\)</span> for <span class="math inline">\(t\)</span> in <span class="math inline">\(0\)</span> to <span class="math inline">\(\pi/6\)</span>.</p>
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<p>The <a href="http://www-history.mcs.st-and.ac.uk/Curves/Astroid.html">astroid</a> is parameterized by <span class="math inline">\(g(t) = a\cos(t)^3\)</span> and <span class="math inline">\(f(t) = a \sin(t)^3\)</span>. Let <span class="math inline">\(a=1\)</span> and rotate the curve from <span class="math inline">\(t=0\)</span> to <span class="math inline">\(t=\pi\)</span> around the <span class="math inline">\(x\)</span> axis. What is the surface area generated?</p>
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<p>For the curve parameterized by <span class="math inline">\(g(t) = a\cos(t)^5\)</span> and <span class="math inline">\(f(t) = a \sin(t)^5\)</span>. Let <span class="math inline">\(a=1\)</span> and rotate the curve from <span class="math inline">\(t=0\)</span> to <span class="math inline">\(t=\pi\)</span> around the <span class="math inline">\(x\)</span> axis. Numerically find the surface area generated?</p>
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