2. For each of the following, compute lIs F . n der.

(a) S is the truncated paraboloid z = x2 + y2, 0 ::; Z ::; 1, n is the outwardpointing normal, and F(x,y,z) = (x,y,z).

(b) S is the truncated half cylinder z = V 4 - y2, 0 ::; x ::; 1, n is outwardpointing normal, and F(x, y, z) = (x2 + y2, yz, z2).

(c) S is the torus in Example 13.32, n is the outward-pointing normal, and F(x,y,z) = (y,-x,z).

(d) S is the portion of z = x2 that lies inside the cylinder x2 + y2 = 1, n is the upward-pointing normal, and F(x, y, z) = (y2 z, cos(2+ log(2 -x2 _y2)), x2 z).