Chapter 6.8, Problem 385E

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.

385. Use the divergence theorem to calculate surface integral ${\displaystyle {\iint }_{s}F\cdot dS}$ , where $F\left(x,y,z\right)=\left(e^{y^2}\right)i+\left(y+\sin \left(z^2\right)\right)j+\left(z-1\right)k$ and S is upper hemisphere $x^2+y^2+z^2=1$ , $z\ge 0$ , oriented upward.