(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the volume integral of the function [tex]f=x^{2}+y^{2}+z^{2}[/tex] over the region inside a sphere of radius R, centered on the origin.

2. Relevant equations

Spherical polars [tex]x=rsin(\theta)cos(\phi), y=rsin(\theta)sin(\phi), z=rcos(\theta)[/tex]

Jacobian in spherical polars = [tex]r^2sin(\theta)[/tex]

3. The attempt at a solution

When i work through it I end up with the triple integral

[tex]V=\int^{R}_{0}dr\int^{\pi}_{-\pi}d\phi\int^{\pi}_{-\pi}d\theta (r^{2}sin^{2}\theta cos^{2}\phi+r^{2}sin^{2}\theta sin^{2}\phi + r^{2}cos^{2}\theta)r^2sin\theta[/tex]

but i'm not too sure whether this is right. Mainly i'm not sure about the limits of integration.

Is this correct please?

Thanks.

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# Surface Integral

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