a) Suppose that E is a two-dimensional region and that S = {(x, y, z) R3: (x, y) E and z = 0}.

a) Suppose that E is a two-dimensional region and that S = {(x, y, z) ˆˆ R3: (x, y) ˆˆ E and z = 0}. Prove that

and that

for each continuous g : E †’ R.
b) Let f : [a, b] †’ R be a Cp function, let C be the curve in R2 determined by z = f{x), a c) Let f: [a, b] †’ R be a Cp function and let S be the surface obtained by revolving the curve y = f(x), a

Area (E) do