What Volume Is Integrated Over for Dipole Moment in Griffiths' Electrodynamics?

Wheelwalker
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In "An Introduction to Electrodynamics", Griffiths gives the following equation for the dipole moment: p=\int r' \rho(r') d\tau'. My question is, in general, what volume am I integrating over? It seems a bit arbitrary to me. I assume I'm integrating over whatever volume is enclosing the charge density \rho(r')?
 
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You are summing over all elements of volume ##\small d\tau'## in all of space. However, there is no need to integrate over those parts of space where the integrand is zero. So, you are correct - you only need to integrate over regions where there is some nonzero charge density.
 
That makes sense to me. Thanks!
 

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