Question

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

Problem here: http://i.imgur.com/pmVPXG3.png

Answer 1

This might be a good resource for you: https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/solid_of_revolution/v/solid-of-revolution-part-6

Answer 2

Refer to the Mathematica v9 item attached.

Answer 3

@robtobey, did you use the washer method for your solution? It looks like you did.

Answer 4

Yes. A disk as a matter of fact.
By the way:\[\int\limits \pi \cos ^2(x)^2 \, dx=\pi \left(\frac{3 x}{8}+\frac{1}{4} \sin (2 x)+\frac{1}{32} \sin (4 x)\right) \]

Answer 5

@robtobey, thank you!

Answer 6

For the revolution around y=1, I think we need to subtract the integral from the volume of the cylinder.