(a) Use Stokes' Theorem to evaluate $\int_C \vec{G} \cdot d\vec{r}$, where $\vec{G}(x, y, z) = (z^2, y^2, xy)$ and C is the triangle with vertices $(1, 0, 0)$, $(0, 1, 0)$ and $(0, 0, 2)$ oriented counterclockwise as viewed from above.
(b) Consider the solid region E enclosed by the cylinder $x^2 + y^2 = 4$ and the planes $z = 0$ and $z = 1$. Use the Divergence Theorem to evaluate $\iint_S \vec{F} \cdot d\vec{S}$, where $\vec{F}(x, y, z) = (xy^2 + e^{-x^2})\vec{i} + (x^2y + \arctan(xz^2))\vec{j} + (x^2y + x^2z^2 + y^2z^2)\vec{k}$. and S is the boundary of the region E.
