2. For each of the following, evaluate I Is curl F . nda.

(a) 8 is the "bottomless" surface in the upper half space z 2 ° bounded by y = x2, Z = 1 - y, n is the outward-pointing normal, and F(x,y,z) =

(xsinz3,ycosz3,x3 +y3 +z3).

(b) 8isthetruncatedparaboloidz = 3-x2_y2, z 20,nistheoutward-pointing normal, and F(x, y, z) = (y, xyz, y).

(c) 8 is the hemisphere z = .)10 - x2 - y2, n is the inward-pointing normal, and F(x, y, z) = (x, x, x2y310g(z + 1)).

(d) 8 is the "bottomless" tetrahedron in the upper half space z 2 ° bounded by x = 0, y = 0, x + 2y + 3z = 1, z 2 0, n is the outward-pointing normal, and F(x,y,z) = (xy,yz,xz).