Chapter 13.7, Problem 54E

Ellipsoid problems Let D be the solid bounded by the ellipsoid x²/a² + y²/b² + z²/c² = 1, where a > 0, b > 0, and c > 0 are real numbers. Let T be the transformation x = au, y = bv, z = cw.

54.    Evaluate ${\displaystyle \underset{D}{\iiint }\left|xyz\right|dA.}$