Chapter 6.8, Problem 386E

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.

386. Use the divergence theorem to calculate surface integral ${\displaystyle {\iint }_{s}F\cdot dS}$ , where $F\left(x,y,z\right)=x^{4}i-x^3{z}^{2}j+4x{y}^{2}zk$ and S is the surface bounded by cylinder $x^2+y^2=1$ and planes $z=x+2$ and $z=0$ .