Chapter 6.8, Problem 377E

For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral ${\displaystyle {\int }_{s}F\cdot ndS}$ for the given choice of F and the boundary surface S. For each closed surface, assume N is the outward unit normal vector.

377. [T] $F\left(x,y,z\right)=\left(\cos yz\right)i+e^{xz}j+3z^{2}k$ ; S is the surface of hemisphere $z=\sqrt{4-x^2-y^2}$ together with disk $x^2+y^2\le 4$ in the xy-plane.