= Scalar surface integral
{title2=$\int_S f\,dS$}
A <scalar surface integral> integrates a <scalar field> against the unsigned <surface area element>. For a regular <parametrization> $\mathbf r(u,v)$, it is $\int f(\mathbf r(u,v))\|\mathbf r_u\times\mathbf r_v\|\,du\,dv$. Reversing orientation does not change it. For example, the <scalar surface integral> of the constant one is the <surface area>; a signed <flux> instead integrates the <normal component> of a <vector field>.
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