I am trying to evaluate the following:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\iiint_{V} (16x^2 + 9y^2 + 4z^2)^{1/4} \,dx\,dy\,dz

[/tex]

Where V is the ellipsoid [tex]16x^2 + 9y^2 + 4z^2 \leq 16[/tex]

This is what i've done:

Change of variables with

[tex]

u^2 = 16x^2

[/tex]

[tex]

v^2 = 9y^2

[/tex]

[tex]

w^2 = 4z^2

[/tex]

Then V is the sphere

[tex]u^2 + v^2 + z^2 \leq 16[/tex]

And the jacobian is

[tex]\frac{1}{24}[/tex]

Than another Change of variables to Spherical cordinates, so the resulting integral is:

[tex]\int_{0}^{2\pi} \int_{0}^{pi} \int_{0}^{4} (\rho^2)^{1/4}\rho^2\sin\phi\frac{1}{24} \,d\rho\, d\phi\, d\theta[/tex]

My question is if I am going about this the correct way and if it is ok to make two change of variables as I have done. Thanks.

Steve

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# Triple integral

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