Suppose $\vec{F}(x,y) = \langle x^2 + 3 y, \, 5 x - 3 y^2 \rangle$. Use Green's Theorem to calculate the circulation of $\vec{F}$ around the perimeter of the triangle $C$ oriented counter-clockwise with vertices $(6,0)$, $(0,3)$, and $(-6,0)$.

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