For each of the following, evaluate S F-nd, where n is the outward-pointing normal. a) S is

Question:

For each of the following, evaluate ∫∫S F-ndσ, where n is the outward-pointing normal.
a) S is the topological boundary of the rectangle [0, 1] × [0, 2] × [0, 3] and F(x, y, z) - (x + ez, y + ez, ez).
b) S is the truncated cylinder x2 + y2 = 1, 0 < z < 1 together with the disks x2 + y2 < 1, z = 0, 1, and F(x, y, z) = (x2, y2, z2).
c) S is the topological boundary of E, where E ⊂ R3 is bounded by z = 2 - x2, z = x2, y = 0, z = y, and F(x, y, z) = (x + f(y, z), y + g(x, z),z + h(x, y)) and f, g, h : R2 → R are C.
d) S is the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 and F(x, y, z) = (x|y|, y|z|, z|x|).