( 887, #17) Use the transformation x = a u, y = b v, z = c w to evaluate the integral

where E is the solid enclosed by the ellipsoid

( This integral gives the volume of the ellipsoid.)

Solution:From the given equations we have:

Thus, the image S of the original domain E is a sphere of radius 1:

Our Jacobian is:

Consequently

The last equation follows from the fact that a sphere of radius 1 has volume (4/3) Pi.

by: nl