Chapter 6.8, Problem 380E

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.

380. [T] $F\left(x,y,z\right)=x^{2}i+y^{2}j+z^{2}k$ ; S is the surface of sphere $x^2+y^2+z^2=4$ .