Volume of bounded region

Question

I would like to find the volume of the region bounded by:

$x^2 + y^2 = 1$

I just need help setting up the integral. Any and all help is greatly appreciated. Thank you!

My work thus far:

$V = \int_0^{2 \pi} \int _0 ^1 \int _ {r^2(1+2sin2 \theta)} ^ {4-r^2(1+2sin2 \theta)}rdzdrd \theta$

Answer 1

First find the intersection of the the two surfaces, to find $$ x^2+y^2 =1.$$

Then set up the integral in cylindrical coordinates.

$$ V= \int _0^{2\pi} \int _0^1 \int _{r^2(1+2\cos ^2 \theta)} ^{4-r^2(1+2\sin ^2 \theta)} dzr dr d \theta $$