Template:Iiint

The following documentation is located at Template:Iiint/doc. [<Edit> Template:Iiint/doc]
[⧼Purge⧽ Template:Iiint]

The {{iiint}} mathematical formatting template calls the {{integral}} template with the type argument set to iiint or [the nicer looking] 3int (triple integral).

Usage

{{iiint|lower limit|upper limit|integrand}}

or

{{iiint|lower limit|upper limit|integrand|format}}

or

{{iiint|lower limit|upper limit}} integrand

or

{{iiint|lower limit|upper limit|format}} integrand

where format is among:

• htm: text style HTML+CSS (default);
• tex: text style LaTeX;
• HTM: display style HTML+CSS;
• TEX: display style LaTeX.

Examples

The code

: {{repeat|2|{{repeat|15|yadda{{nbsp}}}}{{nl}}}}before <!--
-->{{math|{{iiint|''D''}} ''f''{{sp|2}}(''x'', ''y'', ''z'') {{d|''x''}}{{sp|3}}{{d|''y''}}{{sp|3}}{{d|''z''}}{{sp|1}} {{=}} <!--
-->{{iiint|''T''}} ''f''{{sp|2}}({{sp|2}}''{{Gr|rho}}'' sin ''{{Gr|varphi}}'' cos ''{{Gr|theta}}'', ''{{Gr|rho}}'' sin ''{{Gr|varphi}}'' sin ''{{Gr|theta}}'', ''{{Gr|rho}}'' cos ''{{Gr|varphi}}'') <!--
-->''{{Gr|rho}}''{{^|2}} sin ''{{Gr|varphi}}''{{sp|3}}{{d|''{{Gr|rho}}''}}{{sp|3}}{{d|''{{Gr|theta}}''}}{{sp|3}}{{d|''{{Gr|varphi}}''}}. 
|tex = \iiint_{D} f(x, y, z) \, dx \, dy \, dz = \iiint_{T} f( \rho \sin \varphi \cos \theta , \rho \sin \varphi \sin \theta , \rho \cos \varphi ) \, \rho^{2} \sin \varphi \, d\rho \, d\theta \, d\varphi .
|&}} after{{repeat|2|{{nl}}{{repeat|15|yadda{{nbsp}}}}}}

yields the text style HTML+CSS

yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda 
yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda 
before

∫ ∫ ∫ D D   f  (x, y, z) d x d y d z  = ∫ ∫ ∫ T T   f  (  ρ sin φ cos θ, ρ sin φ sin θ, ρ cos φ) ρ 2 sin φ d ρ d θ d φ.

after
yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda 
yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda 

and with the $ option, yields the text style LaTeX

yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda 
yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda 
before $\textstyle {\iiint _{D}f(x,y,z)\,dx\,dy\,dz=\iiint _{T}f(\rho \sin \varphi \cos \theta ,\rho \sin \varphi \sin \theta ,\rho \cos \varphi )\,\rho ^{2}\sin \varphi \,d\rho \,d\theta \,d\varphi .}$ after
yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda 
yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda 

The code

: {{math|{{iiint|''D''||HTM}} ''f''{{sp|2}}(''x'', ''y'', ''z'') {{d|''x''}}{{sp|3}}{{d|''y''}}{{sp|3}}{{d|''z''}}{{sp|1}} {{=}} <!--
-->{{iiint|''T''||HTM}} ''f''{{sp|2}}({{sp|2}}''{{Gr|rho}}'' sin ''{{Gr|varphi}}'' cos ''{{Gr|theta}}'', ''{{Gr|rho}}'' sin ''{{Gr|varphi}}'' sin ''{{Gr|theta}}'', ''{{Gr|rho}}'' cos ''{{Gr|varphi}}'') <!--
-->''{{Gr|rho}}''{{^|2}} sin ''{{Gr|varphi}}''{{sp|3}}{{d|''{{Gr|rho}}''}}{{sp|3}}{{d|''{{Gr|theta}}''}}{{sp|3}}{{d|''{{Gr|varphi}}''}}. 
|tex = \iiint_{D} f(x, y, z) \, dx \, dy \, dz = \iiint_{T} f( \rho \sin \varphi \cos \theta , \rho \sin \varphi \sin \theta , \rho \cos \varphi ) \, \rho^{2} \sin \varphi \, d\rho \, d\theta \, d\varphi .
|&&}}

yields the display style HTML+CSS

∫ ∫ ∫ D D f  (x, y, z) d x d y d z  = ∫ ∫ ∫ T T f  (  ρ sin φ cos θ, ρ sin φ sin θ, ρ cos φ) ρ 2 sin φ d ρ d θ d φ.

and with the $ option, yields the display style LaTeX

${\begin{array}{l}\displaystyle {\iiint _{D}f(x,y,z)\,dx\,dy\,dz=\iiint _{T}f(\rho \sin \varphi \cos \theta ,\rho \sin \varphi \sin \theta ,\rho \cos \varphi )\,\rho ^{2}\sin \varphi \,d\rho \,d\theta \,d\varphi .}\end{array}}$

Code

{{integral|3int<!--iiint-->|{{{1|}}}|{{{2|}}}|{{{3|}}}|{{{4|}}}}}

See also

• {{integral}} (type argument: int, iint, iiint, iiiint, idotsint, oint, varointclockwise, ointctrclockwise, oiint, oiiint)

• {{int}} (simple integral: {{integral}} with int as type argument)
• {{iint}} (double integral: {{integral}} with iint as type argument)
• {{iiint}} (triple integral: {{integral}} with iiint as type argument)
• {{iiiint}} (quadruple integral: {{integral}} with iiiint as type argument)
• {{idotsint}} (multiple integral: {{integral}} with idotsint as type argument)

• {{oint}} ([closed] path integral: {{integral}} with oint as type argument)
• {{varointclockwise}} ([closed] clockwise path integral: {{integral}} with varointclockwise as type argument)
• {{ointctrclockwise}} ([closed] counterclockwise path integral: {{integral}} with ointctrclockwise as type argument)
• {{oiint}} ([closed] surface integral: {{integral}} with oiint as type argument)
• {{oiiint}} ([closed] hypersurface integral: {{integral}} with oiiint as type argument)

• {{sum}} (summation)
• {{prod}} (product)

External links

• Template:Intorient—Wikipedia.org.

• {{sum}} (summation)
• {{prod}} (product)