Chapter 6.8, Problem 403E

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.

403. Use the divergence theorem to find the outward flux of field $F\left(x,y,z\right)=\left(x^3-3y\right)i+\left(2yz+1\right)j+xyzk$ through the cube bounded by planes $x=\pm 1$ , $y=\pm 1$ , and $z=\pm 1$ .