Chapter 6.8, Problem 402E

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.

402. Let $F\left(x,y,z\right)=2xi-3xyj+x{z}^{2}k$ . Use the divergence theorem to calculate ${\displaystyle {\iint }_{s}F\cdot dS}$ , where S is the surface of the cube with corners at $\left(0,0,0\right)$ , $\left(1,0,0\right)$ , $\left(0,1,0\right)$ , $\left(1,1,0\right)$ , $\left(0,0,1\right)$ , $\left(1,0,1\right)$ , $\left(0,1,1\right)$ , and $\left(1,1,1\right)$ , oriented outward.