daviddoji/CalculusWithJuliaNotes.jl
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use quarto, not Pluto to render pages

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jverzani
2022-07-24 16:38:24 -04:00
parent 93c993206a
commit 7b37ca828c
879 changed files with 793311 additions and 2678 deletions
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CwJ/integrals/area_between_curves.jmd
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@@ -317,13 +317,9 @@ g1(y)=exp(y)-1 # y=log(x+1) so e^y = x + 1, x = e^y - 1
quadgk(y -> f1(y) - g1(y), a1, b1)[1]
```
```julia; echo=false
note("""
!!! note
When doing problems by hand this latter style can often reduce the complications, but when approaching the task numerically, the first two styles are generally easier, though computationally more expensive.
When doing problems by hand this latter style can often reduce the complications, but when approaching the task numerically, the first two styles are generally easier, though computationally more expensive.
""")
```
#### Integrating in different directions
@@ -427,7 +423,7 @@ Find the area enclosed by the curves $y=2-x^2$ and $y=x^2 - 3$.
```julia; hold=true; echo=false
f(x) = 2 - x^2
g(x) = x^2 - 3
a,b = find_zeros(x -> f(x) - g(x), -10,10)
a,b = find_zeros(x -> f(x) - g(x), -10, 10)
val, _ = quadgk(x -> f(x) - g(x), a, b)
numericq(val)
```
@@ -569,16 +565,12 @@ Is the guess that the entire sculpture is more than two tons?
```julia; hold=true; echo=false
choices=["Less than two tons", "More than two tons"]
ans = 2
radioq(choices, ans, keep_order=true)
```
```julia; hold=true; echo=false
note("""
We used area to estimate weight in this example, but Galileo used weight to estimate area. It is [mentioned](https://www.maa.org/sites/default/files/pdf/cmj_ftp/CMJ/January%202010/3%20Articles/3%20Martin/08-170.pdf) by Martin that in order to estimate the area enclosed by one arch of a cycloid, Galileo cut the arch from from some material and compared the weight to the weight of the generating circle. He concluded the area is close to ``3`` times that of the circle, a conjecture proved by Roberval in 1634.
""")
answ = 2
radioq(choices, answ, keep_order=true)
```
!!! note
We used area to estimate weight in this example, but Galileo used weight to estimate area. It is [mentioned](https://www.maa.org/sites/default/files/pdf/cmj_ftp/CMJ/January%202010/3%20Articles/3%20Martin/08-170.pdf) by Martin that in order to estimate the area enclosed by one arch of a cycloid, Galileo cut the arch from from some material and compared the weight to the weight of the generating circle. He concluded the area is close to ``3`` times that of the circle, a conjecture proved by Roberval in 1634.
###### Question