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Template:Intorient

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$\ointclockwise$

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This template is used to include the oriented integrals around closed surfaces (or hypersurfaces in higher dimensions), usually in a mathematical formula. They are additional symbols to the non-oriented integrals\oiint and \oiiint which are not yet rendered on Wikipedia.

Arguments

[edit]

preintegral the text or formula immediately before the integral
symbol the integral symbol,

Select one of...	Arrow up, integrals over a closed			Arrow down, integrals over a closed
Select one of...	1-surface	2-surface	3-surface	1-surface	2-surface	3-surface
Clockwise orientation	oint = $\oiint$	oiint = $\oiint$	oiiint = $\oiint$	varoint = $\oiint$	varoiint = $\oiint$	varoiiint = $\oiint$
Counterclockwise orientation	ointctr = $\oiint$	oiintctr = $\oiint$	oiiintctr = $\oiint$	varointctr = $\oiint$	varoiintctr = $\oiint$	varoiiintctr = $\oiint$

The default is $\oiint$

intsubscpt the subscript below the integral
integrand the text or formula immediately after the formula

All parameters are optional.

Examples

[edit]

The work done in athermodynamic cycle on anindicator diagram: $W=$ $\varointclockwise$ ${\scriptstyle \Gamma }$ $p\,{\rm {d}}V$

{{intorient| preintegral=<math>W =</math>| symbol= varoint| intsubscpt=<math>{\scriptstyle\Gamma}</math>| integrand=<math>p\,{\rm d}V</math>}}

Incomplex analysis forcontour integrals: $\varointclockwise$ ${\scriptstyle \Gamma }$ ${\frac {{\rm {d}}z}{(z+a)^{3}\,z^{1/2}}}$

{{intorient|| preintegral=| symbol= varoint| intsubscpt=<math>{\scriptstyle\Gamma}</math>| integrand=<math>\frac{{\rm d}z}{(z+a)^3\, z^{1/2}}</math>}}

Line integrals of vector fields: $\ointclockwise$ ${\scriptstyle \partial S}$ $\mathbf {F} \cdot {\rm {d}}\mathbf {r} =-$ $\ointctrclockwise$ ${\scriptstyle \partial S}$ $\mathbf {F} \cdot {\rm {d}}\mathbf {r}$

{{intorient|<!-- You have to nest things this way to insure everything stays in one line. -->| preintegral={{intorient|| preintegral=| symbol= oint| intsubscpt=<math>{\scriptstyle\partial S}</math>| integrand=<math>\mathbf{F}\cdot{\rm d}\mathbf{r} = -</math>}}|symbol=ointctr| intsubscpt=<math>{\scriptstyle\partial S}</math>| integrand=<math>\mathbf{F}\cdot{\rm d}\mathbf{r}</math>}}

Other examples: $\oiintclockwise$ ${\scriptstyle \Sigma }$ $(E+H\wedge T)\,{\rm {d}}^{2}\Sigma$

{{Intorient|| preintegral=| symbol= oiiintctr| intsubscpt=<math>{\scriptstyle\Sigma}</math>| integrand=<math>(E + H\wedge T)\,{\rm d}^2\Sigma</math>}}

$\varoiiintctrclockwise$

{\scriptstyle \Omega }

(E+H\wedge T)\,{\rm {d}}^{4}\Omega

{{Intorient|| preintegral=| symbol= varoiiintctr| intsubscpt=<math>{\scriptstyle\Omega}</math>| integrand=<math>(E + H\wedge T)\,{\rm d}^4\Omega</math>}}

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Arguments

Examples

See also