Chapter 17, Problem 54RE

Three methods Find the surface area of the paraboloid z = x² + y², for 0 ≤ z ≤ 4, in three ways.

a.    Use an explicit description of the surface.

b.    Use the parametric description r = 〈v cos u, v sin u, v²).

c.    Use the parametric description $r=\langle \sqrt{v}\cos u,\sqrt{v}\sin u,v\rangle$.