Chapter 6.8, Problem 413E

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.

413. Find ${\displaystyle {\iint }_{s}F\cdot dS}$ , where $F\left(x,y,z\right)=xi+yj+zk$ and S is the outwardly oriented surface obtained by removing cube $\left[1,2\right]\times \left[1,2\right]\times \left[1,2\right]$ from cube $\left[0,2\right]\times \left[0,2\right]\times \left[0,2\right]$ .