Contents

Template:Intorient

• 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
	1-surface	2-surface	3-surface	1-surface	2-surface	3-surface
Clockwise orientation	oint =	oiint =	oiiint =	varoint =	varoiint =	varoiiint =
Counterclockwise orientation	ointctr =	oiintctr =	oiiintctr =	varointctr =	varoiintctr =	varoiiintctr =

The default is

• 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 a thermodynamic cycle on an indicator diagram: ${\displaystyle W=}$ ${\displaystyle {\scriptstyle \Gamma }}$ ${\displaystyle p\,{\rm {d}}V}$

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

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

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

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

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

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

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

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

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

See also[edit]

Non-oriented boundary integrals over a 2-surface and 3-surface can be implemented respectively by:

• {{Oiint}}
• {{Oiiint}}

These symbols are currently not supported in MediaWiki's Math mode and this feature request is tracked in phab:T182127.