6. For each of the following, find a (piecewise) smooth parametrization of G and compute fegds.

(a) G is the curve y = J9 - X2, x ~ 0, and g(x, y) = xy2.

(b) G is the portion of the ellipse x2/a2 + y2/b2 = 1,

a, b > 0, which lies in the first quadrant and g(x, y) = xy.

(c) G is the intersection of the surfaces x2 + Z2 = 4 and y = x2, and g( x, y, z) =

VI +yz2.

(d) G is the triangle with vertices (0,0,0), (1,0,0), and (0,2,0), and g(x, y, z) =

X+y+Z3.