\[\iint_{S}f(x,y,z)\,\mathrm{d}S=\iint_{D}f(\boldsymbol{{\Phi}}(u,v))\left\|{%
\mathbf{T}_{u}\times\mathbf{T}_{v}}\right\|\,\mathrm{d}u\,\mathrm{d}v.\]