1. ## Volume of revolution

Find the area of the region in the first quadrant bounded by the graph of y^2=4x^2-x^4 and the x-axis. Find the volume of the solid obtained by revolving this region about the x-axis.

With y=squareroot(4x^2-x^4) I was just going to find the integral of y=4x^2-x^4 from [0,2]. Is that right?

2. Yes, but don't forget to multiply by $\pi$!

You want to evaluate $\pi\int_0^2 4x^2-x^4\,dx$

3. Yes of course! Always with revolution you need a pi except the shell method where you need 2pi. Thanks =)

4. But it's hard to figure out the graph of $y^2=4x^2-x^4$.