Chapter 6.8, Problem 389E

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.

389. [T] Use a CAS and the divergence theorem to calculate flux ${\displaystyle {\iint }_{s}F\cdot dS}$ , where $F\left(x,y,z\right)=\left(x^3+y^3\right)i+\left(y^3+z^3\right)j+\left(z^3+x^3\right)k$ and S is a sphere with $\left(0,0\right)$ and radius 2.