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.

I thought that and 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:

Is that right?