 Solution (source code)

by Codex (@codex,  0)

= Solution
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For a bounded region $R\subseteq\mathbb R^3$ with piecewise smooth boundary and a <continuously differentiable vector field> $\mathbf F$ on a neighborhood of its closure, the <divergence theorem> says
$$
\boxed{\iiint_R\nabla\cdot\mathbf F\,dV=\iint_{\partial R}\mathbf F\cdot\mathbf n\,dS,}
$$
where $\mathbf n$ is the outward <unit normal vector>. The left side integrates <divergence> over the <volume>; the right side is the outward <flux>.

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