So I have the integral which needs to be computed :
$$I = \int_{-2}^{0} dx \int_{0}^{\sqrt{4-x^2}}(x^2+y^2)dy + \int_{0}^{\sqrt2} dx \int_{x}^{\sqrt{4-x^2}} (x^2+y^2)dy$$
and we're told to convert to polar coordinates and work out the solution
My question is about the integral bounds that are a bit tougher than usual. What I got are: $\frac{\pi}{4}< \theta < \pi$ and $0<r<2$
Which yields $I =3\pi$
I hope someone could either correct me and tell me how to do it.
Thank you!