Chapter 14, Problem 56RE

Surface area of an ellipsoid Consider the ellipsoid x²/a² + y²/b² + z²/c² = 1, where a, b, and c are positive real numbers.

a.    Show that the surface is described by the parametric equations

r(u, v) = 〈a cos u sin v, b sin u sin v, c cos v〉

for 0 ≤ u ≤ 2π, 0 ≤ v ≤ π.

b.    Write an integral for the surface area of the ellipsoid.