3. For each of the following, evaluate I Is F ·nda using Stokes's Theorem or Gauss's Theorem.

(a) S is the sphere x2 + y2 + z2 = 1, n is the outward-pointing normal, and F(x,y,z) = (xz2,x2y- z3,2xy+y2z).

(b) S is the portion of the plane z = y that lies inside the ball B1(O), n is the upward-pointing normal, and F(x, y, z) = (xy, xz, -yz).

(c) S is the truncated cone y = 2v'X2 + z2, 2 ~ y ~ 4, n is the outward-pointing normal, and F(x, y, z) = (x, -2y, z).

(d) S is a union of truncated paraboloids z = 4 - x2 - y2, ° ~ z ::s 4, and z = x2 + y2 - 4, -4 ~ z ~ 0, n is the outward-pointing normal, and F( x, y, z) = (x + y2 + sin z, x + y2 + 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).