= Solution
{c}
One sufficient version of the <divergence theorem> is the following. Let $R$ be a bounded region in $\mathbb R^3$ with a closed, piecewise <smooth surface> as its boundary, and let $\mathbf F$ be a <continuously differentiable function> with values in $\mathbb R^3$ on an open neighbourhood of the <closure> of $R$. With $\mathbf n$ the outward <unit normal vector>,
$$
\boxed{\iiint_R\nabla\cdot\mathbf F\,dV
=\iint_{\partial R}\mathbf F\cdot\mathbf n\,dS}.
$$
The boundary <surface integral> is the total outward <flux integral>. If the boundary has several components, each has the outward <orientation> relative to the material of $R$; inner components therefore point into the holes. Edges and isolated vertices may be omitted when assigning the <unit normal vector>, since they have zero <surface area>.
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