Consider the vector field F(x, y, z)=(3xy, 4x2, -3yz+6) Consider also the 3-dimensional region D bounded by the surface S S₁US₂ where 1 = • S₁ = {(x, y, 0) | x² + y² ≤ 1}, the unit disc in the plane z = 0, with boundary circle C = {(x, y, 0) | x² + y² = 1}. S₂ = {(x, y, 1x2 − y²) | x² + y² ≤ 1}, an upside down paraboloid with the same boundary circle C. To visualize all this, think of a bullet standing on its flat end. Let n denote the outward pointing unit normal vector on S. (Note that ñ is only piecewise continuous: it is discontinuous along the common boundary circle C of S₁ and S2; but piecewise continuity is just fine, as it is in Green's Theorem). (a) Verify that divF = 0. (b) Use the divergence theorem to calculate JJ FdS where n is the outward pointing unit normal vector on the surface S. (c) Calculate the surface integral ffs, F.ñ dS using a double integral (Hint: What are the values of F(x, y, z) and of n on the plane z = 0?) (d) Use your previous results to write down the value of the surface integral f√s, F. ñ ds. (Hint: In this problem, there are almost no actual integrals that you have to calculate. If you find yourself buried deep in the calculation of some multiple integral, you are doing it wrong).