Chapter 6.8, Problem 383E

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.

383. [T] $F\left(x,y,z\right)=x^{3}i+y^{3}j+3a^{2}zk\left(\text{constant a}>0\right)$ ; S is the surface bounded by cylinder $x^2+y^2=a^2$ and planes $z=0$ and $z=1$ .