For each of the following, evaluate S F - nd using Stokes's Theorem or the Divergence Theorem.

Question:

For each of the following, evaluate ∫∫S F - ndσ using Stokes's Theorem or the Divergence Theorem.
a) S is the sphere x2 + y2 + z2 = 1, n is the outward-pointing normal, and ¥(x, y, z) = (xz2, x2y - z3, 2xy + y2z).
b) S is the portion of the plane z = y which lies inside the ball B1(0), n is the upward pointing normal, and F(x, y, z) = (xy, xz, - yz).
c) S is the truncated cone y = 2√x2 + z2, 2 < y < 4, n is the outward-pointing normal, and F(x, y, z) = U, - 2y, z).
d) S is a union of truncated paraboloids z = 4 - x2 - y2, 0 < z < 4, and z = x2 + y2 - 4, -4 < z < 0, n is the outward-pointing normal, and
F(x, y, z) = (x + y + sin z, x + y + cos z, cos x + sin y + z).
e) S is the union of three surfaces z = x2 + y2 (0 < z < 2), 2 = x2 + y2 (2 < z < 5), and z = 7 - x2 - y2 (5 < z < 6), n is the outward-pointing normal, and F(x, y, z) = (2y, 2z, 1).