I'm asked to find the following integral by using Green's theorem: $$ I=\iint_D \frac{2ay-y^2-x^2}{y}dxdy $$ where $D$ is the region enclosed by the curve $x^2+y^2=2ay$ and $y\geq a$.
The only thing they taught me, in theory, was the statement of the theorem so I have no idea where to start solving this exercise. If someone can show me how to start or show a meaningful example I would appreciate it.