# Skabelon:Intorient

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Skabelondokumentation[vis] [redigér] [historik] [opfrisk]

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 \oiint and \oiiint which are not yet rendered on wikipedia.

## Arguments

• 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

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

{{intorient
| preintegral=$W=$
| symbol = varoint
| intsubscpt = ${\scriptstyle \Gamma}$
| integrand = $p{\rm d}V$
}}
• In complex analysis for contour integrals: ${\displaystyle {\scriptstyle \Gamma }}$${\displaystyle {\frac {{\rm {d}}z}{(z+a)^{3}z^{1/2}}}}$

{{intorient|
| preintegral =
|symbol=varoint
| intsubscpt = ${\scriptstyle \Gamma}$
| integrand = $\frac{{\rm d}z}{(z+a)^3z^{1/2}}$
}}
• 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|
| preintegral = {{intorient|
| preintegral =
|symbol=oint
| intsubscpt = ${\scriptstyle \partial S}$
| integrand = $\mathbf{F}\cdot{\rm d}\mathbf{r}=-$
}}
|symbol=ointctr
| intsubscpt = ${\scriptstyle \partial S}$
| integrand = $\mathbf{F}\cdot{\rm d}\mathbf{r}$
}}
• Other examples: ${\displaystyle {\scriptstyle \Sigma }}$${\displaystyle (E+H\wedge T){\rm {d}}^{2}\Sigma }$

{{Intorient|
| preintegral =
|symbol=oiiintctr
| intsubscpt = ${\scriptstyle \Sigma}$
| integrand = $(E+H\wedge T) {\rm d}^2 \Sigma$
}}
${\displaystyle {\scriptstyle \Omega }}$${\displaystyle (E+H\wedge T){\rm {d}}^{4}\Omega }$

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