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Template:Iiint

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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) dxdydz  =
T
T
f  (  ρ sin φ cos θ, ρ sin φ sin θ, ρ cos φ) ρ 2 sin φdρdθdφ.
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 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) dxdydz  =
T
T
f  (  ρ sin φ cos θ, ρ sin φ sin θ, ρ cos φ) ρ 2 sin φdρdθdφ.

and with the $ option, yields the display style LaTeX

Code

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

See also

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




External links