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!

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- Sep 29th 2009, 05:59 AMsinni8volume of the ellipsoid (triple intergral) plz help =)
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! - Sep 29th 2009, 06:09 AMKrizalid
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 $\displaystyle \frac43\pi abc.$