2. For each of the following, find a (piecewise) smooth parametrization of Sand of as, and compute I Is 9 dO".

(a) S is the portion of the surface z = x2 - y2 that lies above the xy plane and between the planes x = 1 and x = -1, and g(x,y,z) = VI +4x2 +4y2.

(b) S is the surface y = x3, 0::; y::; 8,0::; z::; 4, and g(x,y,z) = x3z.

(c) S is the portion of the hemisphere z = V9 - x2 - y2 that lies outside the cylinder 2x2 + 2y2 = 9, and g(x, y, z) = x + y + z.