Why is the volume integral of zero equal to zero?

[tomwilliam2]

If the integral of zero is a constant, then why is the volume integral of zero just zero?

 

[dextercioby]

You're addressing two types of integration. <Volume integrals> can be expressed as interated definite integration, while <integral of 0 is a constant> means that you're speaking of indefinite integration.

 

[Mandelbroth]

If the integral of zero is a constant, then why is the volume integral of zero just zero?

Consider the expression $\displaystyle \iiint\limits_{V}0 \, dV$, which I believe you mean by "volume integral". Since 0 is, itself, a constant, we can pull it out front, getting $\displaystyle 0\iiint\limits_{V} \, dV = 0V = 0$

 

[tomwilliam2]

Thanks, both of you.