Greens theorem but don't know how to start it

Question

Evaluate $\oint \limits _C x \space \mathbb d y$ where $C$ is the circle of center $(0,0)$ and radius $4$, taken once anti-clockwise.

How do I start this question? It doesn't look like any of the forms I've seen for Green's theorem before.

Answer 1

Here $P=0$, $Q=x$. By Green's we have \begin{eqnarray} \oint_C xdy=\int\!\!\!\!\int_R\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}\right)dxdy=\int\!\!\!\!\int dxdy=\text{Area of the circle}=4^2\pi=16\pi \end{eqnarray}