Chapter 6.8, Problem 411E

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.

411. Let E be the solid unit cube with diagonally opposite corners at the origin and $\left(1,1,1\right)$ , and faces parallel to the coordinate planes. Let S be the surface of E, oriented with the outward-pointing normal. Use a CAS to find ${\displaystyle {\iint }_{s}F\cdot dS}$ using the divergence theorem if $F\left(x,y,z\right)=2xyi+3y{e}^{z}j+x\sin zk$ .