Question

How do you find the volume of `y = 11sinx` , `y=0`, `[ 0,pi ]` revolving about the x axis?

Answer 1

`V=121/2pi^2~~597.111`.

Explanation:

This is the formula for calculating the volume of a solid obtained from a revolution around the x-axis:
`V=pi*int_a^b f^2(x) dx`
Our function `f(x)=11sinx and a=0, b=pi`.
So the volume is:
`V=pi*int_0^pi 121sin^2(x) dx`
`V=121pi*int_0^pi sin^2(x) dx`
`V=121pi*[1/2(x-sin(x)cos(x))]_0^pi=121/2pi[x-sin(x)cos(x)]_0^pi`
`V=121/2pi(pi-0-0+0)=121/2pi^2~~597.111`.