Integral of a Surface

Topics: Calculus - Surface

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(definition)

Let $S$ be a surface parametrised by $s(u,v)=\left(s_1(u,v),s_2(u,v),s_3(u,v)\right)$, where $(u,v)\in [a,b]\times [c,d]$.

The integral of this surface is defined as:

$${\iint }_{S}fdS:={\int }_a^b{\int }_c^{d}f(s(u,v))\Vert T_u\times T_v\Vert dvdu$$