10. Gauss' theorem states that

∫∫s F. ds = ∫∫∫v ∇. FdV.

(a) Calculate div F (equivalently ∇.F) for the vector field F = 4xyi - y²j+xzk.

(b) Verify Gauss' theorem for the vector field F in part (a) and the cuboid given by 0 ≤ x ≤ 2, 0≤ y ≤ 3, 0≤z ≤ 4, where S is the surface of the cuboid and
∫∫s F. ds = 96.

(c) Given that the contributions to ∫∫s F. ds from the surfaces with outward pointing normals -i, -j, -k are equal to zero, calculate the individual contributions from the other three surfaces.