Gauss' theorem states that [[F. ds = [[[ V. FdV. (a) Calculate div F (equivalently V-F) for the vector field F = 4xyi − y²j + zzk. (b) Verify Gauss' theorem for the vector field F in part (a) and the cuboid given by 0≤x≤2, 0≤ y ≤3, 0≤ ≤4, where S is the surface of the cuboid and F.ds = 96. (c) Given that the contributions to FdS from the surfaces with outward pointing normals -i, -j,-k are equal to zero, calculate the individual contributions from the other three surfaces.

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