Find the volume of the ellipsoid
x^2/a^2 +y^2/b^2 +z^2/c^2 =1
by solving the triple integral AFTER having made the transformation
x = au, y = bv, and z = cw.
Thanks for ur help!
is a straightforward problem, and the answer is given.
we have $\displaystyle dx\,dy\,dz=abc\,du\,dv\,dw$ and the triple integral is $\displaystyle \iiint\limits_{u^{2}+v^{2}+z^{2}\le 1}{abc\,du\,dv\,dw},$ and this is a unit ball, so the expected volume is $\displaystyle \frac43\pi abc.$