For each of the following, evaluate S using Stokes's Theorem or the Divergence Theorem. a) S

Question:

For each of the following, evaluate ∫S ω using Stokes's Theorem or the Divergence Theorem.
a) S is the topological boundary of cylindrical solid y2 + z2 < 9, 0 < x < 2, with outward pointing normal, and ω = xydydz + (x2 - z2) dz dx + xz dx dy.
b) S is the truncated cylinder x2 + z2 = 8, 0 < y < 1, with outward-pointing normal, and ω = (x - 2z) dydz - y dz dx.
c) S is the topological boundary of R = [0, n/2] × [0, 1] × [0, 3], with outward-pointing normal, and ω = ey cos xdydz + x2z dz dx + (x + y + z)dx dy.
d) S is the intersection of the elliptic cylindrical solid 2x2 + z2 < 1 and the plane x = y, with normal which points toward the positive x-axis, and ω = x dy dz - y dz dx + sin y dx dy.