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Display information for equation id:math.221092.23 on revision:221092

* Page found: Stokes' theorem (eq math.221092.23)

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TeX (original user input):

 \int_{\Sigma} \nabla (\mathbf{F}\cdot \mathrm{d}\mathbf{\Sigma}) -(\nabla\cdot \mathbf{F}) \mathrm{d}\mathbf{\Sigma} = \oint_{\partial\Sigma}  \mathrm{d} \mathbf{r}\times\mathbf{F}.

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Σ ( 𝐅 d 𝚺 ) - ( 𝐅 ) d 𝚺 = Σ d 𝐫 × 𝐅 . subscript Σ 𝐅 d 𝚺 𝐅 d 𝚺 subscript contour-integral Σ differential-d 𝐫 𝐅 {\displaystyle{\displaystyle\int_{\Sigma}\nabla(\mathbf{F}\cdot\mathrm{d}% \mathbf{\Sigma})-(\nabla\cdot\mathbf{F})\mathrm{d}\mathbf{\Sigma}=\oint_{% \partial\Sigma}\mathrm{d}\mathbf{r}\times\mathbf{F}.}}
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SVG (11.487 KB / 3.683 KB) :

integral Underscript normal upper Sigma Endscripts nabla left-parenthesis bold upper F dot normal d times bold upper Sigma right-parenthesis minus left-parenthesis nabla dot bold upper F right-parenthesis times normal d times bold upper Sigma equals contour-integral Underscript partial-differential normal upper Sigma Endscripts normal d bold r times bold upper F period

SVG with PNG fallback (MathML can be enabled via browser plugin) rendering

MathML (2.454 KB / 545 B) :

Σ ( F d Σ ) ( F ) d Σ = Σ d r × F . {\displaystyle \int _{\Sigma }\nabla (\mathbf {F} \cdot \mathrm {d} \mathbf {\Sigma } )-(\nabla \cdot \mathbf {F} )\mathrm {d} \mathbf {\Sigma } =\oint _{\partial \Sigma }\mathrm {d} \mathbf {r} \times \mathbf {F} .}
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    <annotation encoding="application/x-tex">{\displaystyle \int _{\Sigma }\nabla (\mathbf {F} \cdot \mathrm {d} \mathbf {\Sigma } )-(\nabla \cdot \mathbf {F} )\mathrm {d} \mathbf {\Sigma } =\oint _{\partial \Sigma }\mathrm {d} \mathbf {r} \times \mathbf {F} .}</annotation>
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SVG (8.169 KB / 3.27 KB) :

{\displaystyle \int _{\Sigma }\nabla (\mathbf {F} \cdot \mathrm {d} \mathbf {\Sigma } )-(\nabla \cdot \mathbf {F} )\mathrm {d} \mathbf {\Sigma } =\oint _{\partial \Sigma }\mathrm {d} \mathbf {r} \times \mathbf {F} .}

PNG (0 B / 8 B) :


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