Question

Verify that the Divergence Theorem is true for the vector field F on the region

e. Give the flux. F(x, y, z) = 2xi + xyj + 3xzk, E is the cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3.

Answer 1

Here it is.  The verification involves doing it the long way too, which takes 6 surface integrals.  Fortunately each component of the function F is 0 when that variable is 0 so the faces of the cube have no flux at the faces of the cube lying in any coordinate plane.  Let me know if you have questions.