The region Q is bounded by $\displaystyle z=2x^2+y^2$ and $\displaystyle z=2-x^2-y^2$

Ok, I tried using Cartesian coords and got a big mess. Then I tried changing everything to polar coords and got this:

$\displaystyle 2r^2cos^2(\theta)+r^2sin^2(\theta)=2-r^2$

I was hoping that the left side would turn out as nicely as the right side did. Did I do something wrong when converting? Is there something I'm missing? Thanks