How do I integrate the above function over a simple planar polygon in the $z$-plane using Green's theorem? I'm unsure about how to derive the functions $P$ and $Q$ from
\begin{align} \int\!\!\!\!\int_{\Omega} xy \,\,dxdy = \int\!\!\!\!\int_{\Omega} \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \,\,dxdy = \oint_{\partial\Omega} P\ dx + Q \ dy \end{align}