Formula:203

Digital Library of Mathematical Functions ID 1.6.E51

${\displaystyle{\displaystyle A(S)=\iint_{D}\sqrt{1+\left(\frac{\partial f}{\partial x}\right)^{2}+\left(\frac{\partial f}{\partial y}\right)^{2}}\mathrm{d}A.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$: partial derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\partial\NVar{x}}}$: partial differential of $$x$$
• ${\displaystyle{\displaystyle S}}$: parameterized surface
• ${\displaystyle{\displaystyle D}}$: open set in the plane
• ${\displaystyle{\displaystyle A(S)}}$: area of a parameterized smooth surface $$S$$ (locally)
 

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