4. For each of the following, find IIs w, where n is the outward-pointing normal.

(a) S is the topological boundary of the three-dimensional region enclosed by y = x2, Z = 0, z = 1, y = 4, and w = xyzdydz + (x2 + y2 + Z2) dzdx + (x +

y+z)dxdy.

(b) S is the truncated hyperboloid of one sheet x2 - y2 + z2 = 1, ° :::; Y :::; 1, together with the disks x2 + z2 :::; 1, y = 0, and x2 + Z2 :::; 2, y = 1, and w = xYlzl dydz + x21z1 dz dx + (x3 + y3) dx dy.

(c) S is the topological boundary of E, where E c R3 is bounded by the surfaces x2 + y + Z2 = 4 and 4x + y + 2z = 5, and w = (x + y2 + Z2) dy dz + (x2 + y +

z2) dzdx + (x2 + y2 + z) dxdy.