Chapter 6.8, Problem 384E

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.

384. [T] Surface integral ${\displaystyle {\iint }_{s}F\cdot dS}$ , where S is the solid bounded by paraboloid $z=x^2+y^2$ and plane $z=4$ , and $F\left(x,y,z\right)=\left(x+y^2{z}^2\right)i+\left(y+z^2{x}^2\right)j+\left(z+x^2{y}^2\right)k$ .