Find the volume below the surface $z=x^2+y^2$, above the plane $z=0$ and inside the cylinder $x^2+y^2=2y$.
I'm getting the answer as : $$ 2\int_{0}^{2}\int_0^{\sqrt{2y-y^2}}(x^2+y^2)dxdy $$ but I'm not able to solve this integral. Using various tools on the internet, I found the answer to be $\frac{3\pi}{4}$. But the answer given is $\frac{\pi}{2}$. What am I doing wrong?