Divergence Theorem: Understanding and Applying in Vector Calculus

[member 428835]

hey pf! i had a general question with the divergence theorem. specifically, my text writes $$\iint_S \rho \vec{V} \cdot \vec{dS} = \iiint_v \nabla \cdot (\rho \vec{V})$$ where $\rho$ is a scalar, although not necessarily constant! to properly employ the divergence theorem, would i first let $$\rho \vec{V}=\vec{V'}$$ where $\vec{V'}$ is the vector to use the divergence theorem with, thus offering the first written result?

thanks!

 

[arildno]

That is correct.