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# Template:Integral/int/doc

This documentation subpage contains instructions, categories, or other information for Template:Integral/int. [<Edit> Template:Integral/int]

[⧼Purge⧽ Template:Integral/int/doc]

This template is under construction.

Please do not use this unfinished and/or still unreliable template.

(Firefox and Google Chrome and MS Edge: good results! )
(Not the fault of the {{math}} template: MS Edge chops LaTeX PNG's, whether or not we use the {{math}} template! (See #Tests.)

Helper template used by the {{integral}} template to implement the int (simple integral), 2int (double integral), 3int (triple integral), 4int (quadruple integral), and idotsint (multiple integral) options.

## Usage

{{integral/int|from|to|integrand}}

or

{{integral/int|from|to|integrand|format}}

or

{{integral/int|from|to}} integrand

or

{{integral/int|from|to|format}} integrand

## Examples

In the following examples, for HTML+CSS, {{int}} calls the {{integral}} template with the int option, which then uses {{integral/int}} (this template).

The code

: {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|{{int|0|1|''x''{{^|3}}{{sp|3}}{{d|''x''}}}}|&}} and {{math|{{int|0|1}} ''x''{{^|3}}{{sp|3}}{{d|''x''}}|&}} after{{repeat|2|{{nl}}{{repeat|5|yadda{{nbsp}}}}}}

yields the text style HTML+CSS

before
 1 0
x 3dx
and
 1 0
x 3dx
after

The code

: {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|\int_{0}^{1} x^3 dx|$}} after{{repeat|2|{{nl}}{{repeat|5|yadda{{nbsp}}}}}} yields the text style LaTeX yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda before${\displaystyle \textstyle {\int _{0}^{1}x^{3}dx}}$ after yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda The code : {{math|{{int|0|1|''x''{{^|3}}{{sp|3}}{{d|''x''}}|HTM}}|&&}} and {{math|{{int|0|1|HTM}} ''x''{{^|3}}{{sp|3}}{{d|''x''}}|&&}} yields the display style HTML+CSS  1 0 x 3dx and  1 0 x 3dx The code : {{math|\int_{0}^{1} x^3 dx|$$}} yields the display style LaTeX ${\displaystyle {\begin{array}{l}\displaystyle {\int _{0}^{1}x^{3}dx}\end{array}}}$ The code : {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|{{Gr|Gamma}}(''z'') {{=}} <!-- -->{{int|0|infty|''e''{{^|{{op|-}}{{sp|1}}''t''}}{{sp|2}}''t''{{sp|2}}{{^|''z''{{sp|1}}{{op|-}}1}}{{sp|3}}{{d|''t''}}}}|&}} after{{repeat|2|{{nl}}{{repeat|5|yadda{{nbsp}}}}}} yields the text style HTML+CSS yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda before Γ(z) =  ∞ 0 e − t t z − 1dt after yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda The code : {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|\Gamma(z) {{=}} \int_{0}^{\infty} e^{-t} t^{z-1} dt|}} after{{repeat|2|{{nl}}{{repeat|5|yadda{{nbsp}}}}}} yields the text style LaTeX yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda before${\displaystyle \textstyle {\Gamma (z)=\int _{0}^{\infty }e^{-t}t^{z-1}dt}}$ after yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda The code : {{math|{{Gr|Gamma}}(''z'') {{=}} <!-- -->{{int|0|infty|''e''{{^|{{op|-}}{{sp|1}}''t''}}{{sp|2}}''t''{{sp|1}}{{^|''z''{{sp|1}}{{op|-}}1}}{{sp|3}}{{d|''t''}}|HTM}}|&&}} yields the display style HTML+CSS Γ(z) =  ∞ 0 e − t tz − 1dt The code : {{math|\Gamma(z) {{=}} \int_{0}^{\infty} e^{-t} t^{z-1} dt|$$}} yields the display style style LaTeX ${\displaystyle {\begin{array}{l}\displaystyle {\Gamma (z)=\int _{0}^{\infty }e^{-t}t^{z-1}dt}\end{array}}}$ ### \iint and \iiint and \iiiint The code : {{repeat|2|{{repeat|10|yadda{{nbsp}}}}{{nl}}}}<!-- -->before {{math|''F'' {{=}} {{iint|2-ball}} {{d|''F''}}|&}},{{sp|quad}}{{math|''G'' {{=}} {{iiint|3-ball}} {{d|''G''}}|&}},{{sp|quad}}{{math|''H'' {{=}} {{iiiint|4-ball}} {{d|''H''}}|&}} after<!-- -->{{repeat|2|{{nl}}{{repeat|10|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 before F =  2-ball 2-ball dF , G =  3-ball 3-ball dG , H =  4-ball 4-ball dH after yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda The code : {{repeat|2|{{repeat|10|yadda{{nbsp}}}}{{nl}}}}<!-- -->before {{math|F {{=}} \iint_{ \text{2-ball} } dF|$}},{{sp|quad}}{{math|G {{=}} \iiint_{ \text{3-ball} } dG|$}},{{sp|quad}}{{math|H {{=}} \iiiint_{ \text{4-ball} } dH|$}} after<!--


yields the text style LaTeX

before${\displaystyle \textstyle {F=\iint _{\text{2-ball}}dF}}$, ${\displaystyle \textstyle {G=\iiint _{\text{3-ball}}dG}}$, ${\displaystyle \textstyle {H=\iiiint _{\text{4-ball}}dH}}$ after

The code

: {{math|''F'' {{=}} {{iint|2-ball||HTM}} {{d|''F''}}|&&}},{{sp|quad}}{{math|''G'' {{=}} {{iiint|3-ball||HTM}} {{d|''G''}}|&&}},{{sp|quad}}{{math|''H'' {{=}} {{iiiint|4-ball||HTM}} {{d|''H''}}|&&}}

yields the display style HTML+CSS

F =
 2-ball 2-ball
dF
,
G =
 3-ball 3-ball
dG
,
H =
 4-ball 4-ball
dH

The code

: {{math|F {{=}} \iint_{ \text{2-ball} } dF|$$}},{{sp|quad}}{{math|G {{=}} \iiint_{ \text{3-ball} } dG|$$}},{{sp|quad}}{{math|H {{=}} \iiiint_{ \text{4-ball} } dH|$$}}  yields the display style LaTeX ${\displaystyle {\begin{array}{l}\displaystyle {F=\iint _{\text{2-ball}}dF}\end{array}}}$, ${\displaystyle {\begin{array}{l}\displaystyle {G=\iiint _{\text{3-ball}}dG}\end{array}}}$, ${\displaystyle {\begin{array}{l}\displaystyle {H=\iiiint _{\text{4-ball}}dH}\end{array}}}$ ### \idotsint The code : {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|''H'' {{=}} {{idotsint|''n''-ball}} {{d|''H''}}|&}} after{{repeat|2|{{nl}}{{repeat|5|yadda{{nbsp}}}}}} yields the text style HTML+CSS yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda before H =  n-ball n-ball dH after yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda The code : {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|''H'' {{=}} {{idotsint|''n''\text{-ball}||tex}} {{d|''H''|tex}}|}} after{{repeat|2|{{nl}}{{repeat|5|yadda{{nbsp}}}}}} yields the text style LaTeX yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda before${\displaystyle \textstyle {H=\int \!\cdots \!\int _{n{\text{-ball}}}^{}\;d^{}H}}$ after yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda The code : {{math|''H'' {{=}} {{idotsint|''n''-ball||HTM}} {{d|''H''}}|&&}} yields the display style HTML+CSS H =  n-ball n-ball dH The code : {{math|''H'' {{=}} {{idotsint|''n''\text{-ball}||TEX}} {{d|''H''|tex}}|$$}}

yields the display style LaTeX

${\displaystyle {\begin{array}{l}\displaystyle {H=\int \!\cdots \!\int _{n{\text{-ball}}}^{}\;d^{}H}\end{array}}}$

## Tests

The code

: $\int_{0}^{1} x^3 dx$ and {{math|\int_{0}^{1} x^3 dx|$$}} yields the display style LaTeX (Not the fault of the {{math}} template: MS Edge chops LaTeX PNG's, whether or not we use the {{math}} template!) ${\displaystyle \int _{0}^{1}x^{3}dx}$ and${\displaystyle {\begin{array}{l}\displaystyle {\int _{0}^{1}x^{3}dx}\end{array}}}$ The code : $\Gamma(z) = \int_{0}^{\infty} e^{-t} t^{z-1} dt$ and {{math|\Gamma(z) {{=}} \int_{0}^{\infty} e^{-t} t^{z-1} dt|$$}}

yields the display style LaTeX (Not the fault of the {{math}} template: MS Edge chops LaTeX PNG's, whether or not we use the {{math}} template!)

${\displaystyle \Gamma (z)=\int _{0}^{\infty }e^{-t}t^{z-1}dt}$ and${\displaystyle {\begin{array}{l}\displaystyle {\Gamma (z)=\int _{0}^{\infty }e^{-t}t^{z-1}dt}\end{array}}}$