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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 .


yields the text style HTML+CSS

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
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 ${\displaystyle \textstyle {\iiint _{D}f(x,y,z)\,dx\,dy\,dz=\iiint _{T}f(\rho \sin \varphi \cos \theta ,\rho \sin \varphi \sin \theta ,\rho \cos \varphi )\,\rho ^{2}\sin \varphi \,d\rho \,d\theta \,d\varphi .}}$ 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) 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
${\displaystyle {\begin{array}{l}\displaystyle {\iiint _{D}f(x,y,z)\,dx\,dy\,dz=\iiint _{T}f(\rho \sin \varphi \cos \theta ,\rho \sin \varphi \sin \theta ,\rho \cos \varphi )\,\rho ^{2}\sin \varphi \,d\rho \,d\theta \,d\varphi .}\end{array}}}$
{{integral|3int<!--iiint-->|{{{1|}}}|{{{2|}}}|{{{3|}}}|{{{4|}}}}}