Chapter 6.8, Problem 381E

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.

381. [T] $F\left(x,y,z\right)=xi+yj+\left(z^2-1\right)k$ ; S is the surface of the solid bounded by cylinder $x^2+y^2=4$ and planes $z=0$ and $z=1$ .