Have a double integral problem where it wants me to identify the region of integration and then evaluate using polar co-ords.

Given;

I said region of integration is the half circle in the first and fourth quadrants, does this sound correct?

Having identified this region in order to integrate it with polar co-ords i need to specify a range for θ and i'm not sure how to specify θ's range for this region?

i was guessing -pi/2 <= θ <= pi/2 ;

but am really not sure any help here would be appreciated.

(i didn't give function f(x,y) as didnt think it is relevant and have no problems manipulating it for problem)