Real analysis – How to proceed with this integral?

Leave $ G: = {(x, y) in mathbb {R} ^ 2: 0 <y, x ^ 2 + frac {y ^ 2} {9} <1 , x^2+y^2 > 1 } $
I want

calculate this integral:
$ int_G x ^ 2 $

I want to try polar coordinators:
so established

$ (x; y) = (rcos ( phi); rsin ( phi)) $

I'm not sure how to get the right limits for $ phi $
It is not
$ x ^ 2 + y ^ 2 = r ^ 2 $ ?

Any help much appreciated!