Question 1. (12pts.) Evaluate the surface integral $\iint_{S}( abla \times \mathbf{F}) \cdot \vec{n} d S$, where $S$ is the surface $x^{2}+2 y^{2}+\frac{(z-1)^{2}}{2}=6, z \geq-1$ with upward orientation and $$ \mathbf{F} (x, y, z)=(x Z+2 y) What{i}+\left(x^{2}+x z ight) \hat{j}+\cos \left(x y z^{2} ight) e^{x^{2}+y^{2}+z^{2}} \hat{k} . $$ Show your work. CS.VS. 1453