Suppose $\vec{F}(x,y) = 3 y \vec{i} + 5 x y \vec{j}$. Use Green's Theorem to calculate the circulation of $\vec{F}$ around the perimeter of a circle $C$ of radius $2$ centered at the origin and oriented counter-clockwise.

$\displaystyle \int_C \vec{F} \cdot d\vec{r}$ =