Could anyone help me with this exercise? In this subject we are studying integration over surfaces and volumes, 1 and 2-forms and theorems such as Green-Riemann and Gauss-Ostrogradsky, so as Stokes. Yet this formula looks kinda similar to Gauss-Ostrogradsky, I am not able to demonstrate it. Thanks in advance.
Let $D \subset \mathbb{R}^3$ be a compact with $C^1$ boundary and let $f$ be a $C^1$ scalar function defined on $D$. Prove that:
$$ \iint_{\partial D} f \mathrm{d}\overrightarrow{S} = \iiint _D \nabla f\mathrm{d}V. $$