Use Stokes' Theorem to find the circulation of $\vec{F} = \langle xy, yz, xz \rangle$ around the boundary of the surface $S$ given by $z = 4 - x^2$ for $0 \leq x \leq 2$ and $-4 \leq y \leq 4$, oriented upward. Sketch both $S$ and its boundary $C$.

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