Chapter 6.8, Problem 418E

For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D.

418. [T] Use a CAS to compute ${\displaystyle {\iint }_{s}F\cdot dS}$ , where $F\left(x,y,z\right)=xi+yj+2zk$ and S is a part of sphere $x^2+y^2+z^2=2$ with $0\le z\le 1$ .