= Solution
{c}
Let $\Sigma$ be a compact, piecewise smooth <oriented surface> with piecewise smooth boundary, and let $\mathbf F$ be continuously differentiable on an open neighbourhood of $\Sigma$. The <Stokes theorem> states
$$
\boxed{\oint_{\partial\Sigma}\mathbf F\cdot d\mathbf r
=\iint_\Sigma(\nabla\times\mathbf F)\cdot\mathbf n\,dS}.
$$
The <boundary orientation> must agree with the chosen <unit normal vector> by the <right-hand rule>. For an upward <orientation> on a horizontal <disk>, its boundary is traversed counterclockwise when viewed from above. Reversing the <orientation> reverses both the <line integral> and the <surface integral>.
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