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Display information for equation id:math.221346.18 on revision:221346

* Page found: Vector calculus (eq math.221346.18)

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TeX (original user input): 

 \int\!\!\!\!\int_{\Sigma\,\subset\mathbb R^3} \nabla \times \mathbf{F} \cdot d\mathbf{\Sigma} = \oint_{\partial\Sigma} \mathbf{F} \cdot d \mathbf{r}

TeX (checked): 

\int \!\!\!\!\int _{\Sigma \,\subset \mathbb {R} ^{3}}\nabla \times \mathbf {F} \cdot d\mathbf {\Sigma } =\oint _{\partial \Sigma }\mathbf {F} \cdot d\mathbf {r}

LaTeXML (experimental; uses MathML) rendering

MathML (6.896 KB / 1.281 KB) :

∫ ∫ Σ ⊂ ℝ 3 ∇ × 𝐅 ⋅ 𝑑 𝚺 = ∮ ∂ ⁡ Σ 𝐅 ⋅ 𝑑 𝐫 subscript Σ superscript ℝ 3 ⋅ ∇ 𝐅 differential-d 𝚺 subscript contour-integral Σ ⋅ 𝐅 differential-d 𝐫 {\displaystyle\int\!\!\!\!\int_{{\Sigma\,\subset{\mathbb{R}}^{3}}}\nabla\times% {\mathbf{F}}\cdot d{\mathbf{\Sigma}}=\oint_{{\partial\Sigma}}{\mathbf{F}}\cdot d% {\mathbf{r}}} 
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SVG (11.704 KB / 4.338 KB) :

integral integral Underscript normal upper Sigma subset-of double-struck upper R cubed Endscripts nabla times bold upper F dot italic d bold upper Sigma equals contour-integral Underscript partial-differential normal upper Sigma Endscripts bold upper F dot italic d bold r

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

MathML (2.238 KB / 574 B) :

∫ ∫ Σ ⊂ R 3 ∇ × F ⋅ d Σ = ∮ ∂ Σ F ⋅ d r {\displaystyle \int \!\!\!\!\int _{\Sigma \,\subset \mathbb {R} ^{3}}\nabla \times \mathbf {F} \cdot d\mathbf {\Sigma } =\oint _{\partial \Sigma }\mathbf {F} \cdot d\mathbf {r} } 
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SVG (9.463 KB / 4.02 KB) :

{\displaystyle \int \!\!\!\!\int _{\Sigma \,\subset \mathbb {R} ^{3}}\nabla \times \mathbf {F} \cdot d\mathbf {\Sigma } =\oint _{\partial \Sigma }\mathbf {F} \cdot d\mathbf {r} }

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