(6) (bonus question: worth 10 points. total points for assignment not to exceed 100.) use an iterated integral to compute the volume of the ellipsoid x^2/a^2 + y^2/b^2 + z^2/c^2 = 1. the a, b, and c are positive constants.

Let be the ellipsoid with equation



so that the volume of is given by the triple integral



Consider the augmented spherical coordinates given by the identities



Computing the Jacobian, we find that the volume element is given by



so that the volume integral can be written as