Note 1 to entry: For a surface defined by r = f(u, v) where $(u,v)\in \text{U}\subseteq R^{\text{2}}$, the scalar surface element is given by

${\displaystyle \left|\frac{\partial f}{\partial u}\times \frac{\partial f}{\partial v}\right|\cdot \mathrm{d}u\mathrm{d}v}$.

Note 2 to entry: For a surface defined by the equation z = f(x, y), the scalar surface element is given by

$\sqrt{1+{\left(\frac{\partial f}{\partial x}\right)}^2+{\left(\frac{\partial f}{\partial y}\right)}^2}\mathrm{d}x\mathrm{d}y$.