- #1

epiclier

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## Homework Statement

By making two successive simple changes of variables, evaluate:

I =[itex]\int\int\int x^{2} dxdydz[/itex]

inside the volume of the ellipsoid:

[itex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}}=R^{2}[/itex]

## Homework Equations

dxdydz=r^2 Sin(phi) dphi dtheta dr

## The Attempt at a Solution

I will post more here if needed.So I let x=au y=bv z=cw

then I calculated the jacobian which gave |J|=abc

I then manipulated the integral to get:

[itex]a^{3}bc \int\int\int r^{4} sin^{2}(phi}cos{theta} dphi dtheta dr[/itex]

where r is from 0->R

theta is from 0->2π

phi is from 0->π

Following this through got me the answer of:

V=[itex]\frac{a^{3}bc\pi}{2}[/itex]

Would anybody be able to confirm this answer for me?

Thanks in advance!

Epiclier