Chapter 6.8, Problem 408E

For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D.

408. Use the divergence theorem to evaluate ${\displaystyle {\iint }_{s}F\cdot dS}$ , where $F\left(x,y,z\right)=y^{2}zi+y^{3}j+xzk$ and S is the boundary of the cube defined by $-1\le x\le 1$ , $-1\le y\le 1$ , and $0\le z\le 2$ .