use quarto, not Pluto to render pages

CwJ/integrals/surface_area.jmd

@@ -17,7 +17,7 @@ const frontmatter = (
         description = "Calculus with Julia: Surface Area",
         tags = ["CalculusWithJulia", "integrals", "surface area"],
 );
-fig_size=(600, 400)
+fig_size=(800, 600)
 nothing
 ```
 
@@ -174,11 +174,13 @@ formula, even though we just saw how to get this value.
 A cone be be envisioned as rotating the function $f(x) = x\tan(\theta)$ between $0$ and $h$ around the $x$ axis. This integral yields the surface area:
 
 ```math
+\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).
+&= \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*}
 ```
 
 (There are many ways to express this, we used $r$ and $\theta$ to
@@ -449,8 +451,8 @@ choices = [
 "``-\\int_1^{_1} 2\\pi u \\sqrt{1 + u^2} du``",
 "``-\\int_1^{_1} 2\\pi u^2 \\sqrt{1 + u} du``"
 ]
-ans = 1
-radioq(choices, ans)
+answ = 1
+radioq(choices, answ)
 ```
 
 Though the integral can be computed by hand, give a numeric value.
@@ -506,8 +508,8 @@ choices = [
 "``\\int_u^{u_h} 2\\pi y dx``",
 "``\\int_u^{u_h} 2\\pi x dx``"
 ]
-ans = 1
-radioq(choices, ans)
+answ = 1
+radioq(choices, answ)
 ```
 
 ##### Questions