Hey! :o
I want to calculate $\iint_{\Sigma}xdA$ on the triangle with vertices $(1,0,0)$, $(0,1,0)$ and $(0,0,1)$.
We have to define the surface $\Sigma(u,v) = (x(u,v), y(u,v), z(u,v))$ then we get $$\iint_{\Sigma}fdA=\iint_Df(\Sigma(u,v))\|\frac{\partial{\Sigma}}{\partial{u}}(u,v)\times...