Problem 5 Ellipsoidal Spherical Coordinates Consider the ellipsoid W = (1, y, 2 ) : + + where a, b, c are positive constants. Consider the change of variables map T : W* -> W given by T(p. 0, $) = ( apsin() cos(@), bpsin($) sin(0), cp cos($) =I(p,0.) =y(p,8.) =z(p.0.$) These are referred to as ellipsoidal spherical coordinates. (a) What is the region W* in (p, 0, $) space that gets mapped to W? (b) Compute | det DT (p, 0, o)|. Subsequently, use change of variables to find the volume of the ellipsoid given by Vol(W) = 1 drdydz