I am studying fluid mechanics from Landau and Lifshitz and I'm trying to prove the equation $\begin{align*}\\ -\oint \; p\,df = -\int\, grad\,p\,dV\end{align*}\\$ (topic on Euler's equation page 2) which I am running into trouble proving, I was requesting if someone can provide a hint or proof for this equation

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    $\begingroup$ This is a form of the divergence theorem. The notation here is not entirely clear, but it should equate the volume integral of the pressure gradient over a region to the surface integral of the normally directed pressure ($p \mathbf{n}$) over the boundary of the region. Presumably $df$ incorporates the normal vector. This is proved in this answer. $\endgroup$ – RRL Apr 20 '18 at 15:44
  • $\begingroup$ Thanks I was not aware of the analogue of Gauss Divergence Theorem for scalar fields $\endgroup$ – Tom Carter Apr 20 '18 at 18:19

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