Week 13 Discussion

Chapter 7, Question 6

Find the volume of \(y=5x\) from 1 to 2, rotated around the \(x\) axis

\[ R(x)=y=5x\\ \pi\int_1^2(5x)^2dx=\\ \pi\int_1^225x^2dx=\\ \pi\bigg(\frac{25x^3}{3}\bigg|_1^2\bigg)=\\ \pi\bigg(\frac{25\times 8}{3}-\frac{25}{3}\bigg)=\\ =\frac{175\pi}{3}\\ \approx 183.26 \]

in R:

library("stats")
basefunction<-function(x){5*x}
integrand<-function(x){pi*basefunction(x)^2}
integrate(integrand,1,2)

## 183.2596 with absolute error < 2e-12