Question

Find the flux of the vector field F=<3x +2y,−y+z ,2z−x> over the bounding surface of the octahedron with vertices (±1,0,0) ,(0,±1,0) ,(0,0,±1) by

a) direct computation (use symmetry to limit the number of integrals that you actually compute).

b) using Gauss' Theorem (Divergence Theorem)