The curves intersects at and , so using cilindrical shel method, the volume is given by .
You may also see the problem like rotating the area between and about the x-axis from to .
intersection values ...
two symmetrical regions in quads I and III
using the method of washers and taking advantage of symmetry ...
I'm telling you, don't embarrass yourself. You know how to use the calculator for definite integrals right? Try using Abu-Khali's "dx" version and compare it to your own "dy" version. Then try using my own "dy" version and you will see that you are wrong, I promise you.
Edit: Sorry if I sounded like I was flaming you, that's certainly not my intention. It's just that I know I'm right, factually. Try have an open mind.
2nd Edit: yes, pony, you're right, that's the right answer.