Formula:196

Digital Library of Mathematical Functions ID 1.6.E44

${\displaystyle{\displaystyle\iint_{S}\left(\frac{\partial F_{2}}{\partial x}-\frac{\partial F_{1}}{\partial y}\right)\mathrm{d}A=\int_{C}\mathbf{F}\cdot\mathrm{d}\mathbf{s}=\int_{C}F_{1}\mathrm{d}x+F_{2}\mathrm{d}y.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$: partial derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\partial\NVar{x}}}$: partial differential of $$x$$
• ${\displaystyle{\displaystyle S}}$: closed region
• ${\displaystyle{\displaystyle C}}$: closed curve
• ${\displaystyle{\displaystyle F_{j}}}$: vector function components
 

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