Chapter 6.8, Problem 387E

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.

387. Use the divergence theorem to calculate surface integral ${\displaystyle {\iint }_{s}F\cdot dS}$ when $F\left(x,y,z\right)=x^2{z}^{3}i+2xy{z}^{3}j+x{z}^{4}k$ and S is the surface of the box with vertices $\left(\pm 1,\pm 2,\pm 3\right)$ .