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i had a subtlety about the divergence theroem/gradient theorem. specifically, the following was presented: $$ \iint_s p \vec{dS} = \iiint_v \nabla (p) dv$$

i am familiar with the divergence theorem, but that is for a vector "dotted" with a surface element (flux) related to the divergence (expansion) through the volume. i believe the above is the gradient theorem. can anyone verify the legitimacy of this (and perhaps offer some physical intuition if it holds). i should say [itex]p[/itex] is not a constant.

thanks!