Question

What is the volume of the solid generated by rotating about the y-axis the region enclosed by y=sinx and the x-axis, from x=0 to x=π?

Thank you for your help!!

Answer 1

Volume = π[integral] (sin x)^2 dx from 0 to π

The tricky part is to integrate sin^2 x

start with
cos 2x = 1 - 2sin^2 x
sin^2 x = 1/2 - (1/2)cos 2x
= (1/2) (1 - cos 2x)

the integral of that would be (1/2) (x - (1/2)sin 2x)

I am sure you can take it from there

( I got π/2)