Using polar coordinates to solve a double integral

Hi,

I am confused on how to go from rectangular components to polar ones. I'm going to show you the problem I'm trying to solve and the steps I took to solve it. I would really be glad if anyone could take a look and tell me if I'm doing something wrong.

Thanks for viewing,

Bazinga

The question is:

Use polar coordinates to solve the following integral.

$\displaystyle \int^{3}_{-3} \int^{\sqrt{9-y^2}}_{-\sqrt{9-y^2}} e^{-x^2-y^2} \mathrm{d}x\mathrm{d}y$

I thought that $\displaystyle \sqrt{9-y^2}$ and $\displaystyle -\sqrt{9-y^2}$ formed two semi-circles (the positive one in the 1st and 4th quadrant, the other one in the 2nd and 3rd quadrant), which formed a circle.

Then the double integral in polar coordinates would be:

$\displaystyle \int^{2\pi}_{0} \int^{3}_{0} e^{-r^2}r \mathrm{d}r\mathrm{d}\theta$

Is that right?