Verify Gauss' divergence theorem for the flux of the vector field E(x, y, z)=ri+12y j + 3z k which exits through the surface of the box given by B = {(x, y, z) |1 ≤ x ≤ 3,0 ≤ y ≤ 1,3<=<5}. 5 2. Consider the vector field f(x, y, z)=xzi+yzj+x²y²k. Let S be the surface of the sphere of radius VS that is centred at the origin and lies inside the cylinder 2² + y² = 4 for > 0. (a) Carefully sketch S, and identify its boundary OS. (b) By parametrising S appropriately, directly compute the flux integral (f). ds. 2 (c) By computing whatever other integral is necessary (and please be careful about explaining any orien- tation/direction choices you make), verify Stokes' theorem for this case.