Surface Integrals, Stokes & Divergence · Medium problem

Let $\mathbf F = (x^2z - 3y,\ xy + x,\ z^3)$ and let $C$ be the ellipse $\dfrac{x^2}{4} + \dfrac{y^2}{9} = 1$ in the plane $z = 0$, oriented counterclockwise when viewed from above. Use Stokes' theorem to find $\oint_C \mathbf F\cdot d\mathbf r$. Give an exact answer in terms of $\pi$.