Template:Integral/int/doc

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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! Y)
(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

yadda yadda yadda yadda yadda 
yadda yadda yadda yadda yadda 
before 

∫ 1 0  x 3 d x

and 

∫ 1 0   x 3 d x

after
yadda yadda yadda yadda yadda 
yadda yadda yadda yadda yadda 

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$\textstyle {\int _{0}^{1}x^{3}dx}$ 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 3 d x

and

∫ 1 0 x 3 d x

The code

: {{math|\int_{0}^{1} x^3 dx|$$}}

yields the display style LaTeX

${\begin{array}{l}\displaystyle {\int _{0}^{1}x^{3}dx}\end{array}}$

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  − 1 d t

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$\textstyle {\Gamma (z)=\int _{0}^{\infty }e^{-t}t^{z-1}dt}$ 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  t  z  − 1 d t

The code

: {{math|\Gamma(z) {{=}} \int_{0}^{\infty} e^{-t} t^{z-1} dt|$$}}

yields the display style style LaTeX

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

\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   d F

,  

G = ∫ ∫ ∫ 3-ball 3-ball   d G

,  

H = ∫ ∫ ∫ ∫ 4-ball 4-ball   d H

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<!--
-->{{repeat|2|{{nl}}{{repeat|10|yadda{{nbsp}}}}}}

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

The code

: {{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 d F

, 

G = ∫ ∫ ∫ 3-ball 3-ball d G

, 

H = ∫ ∫ ∫ ∫ 4-ball 4-ball d H

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

${\begin{array}{l}\displaystyle {F=\iint _{\text{2-ball}}dF}\end{array}}$, ${\begin{array}{l}\displaystyle {G=\iiint _{\text{3-ball}}dG}\end{array}}$, ${\begin{array}{l}\displaystyle {H=\iiiint _{\text{4-ball}}dH}\end{array}}$

\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   d H

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$\textstyle {H=\int \!\cdots \!\int _{n{\text{-ball}}}^{}\;d^{}H}$ 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 d H

The code

: {{math|''H'' {{=}} {{idotsint|''n''\text{-ball}||TEX}} {{d|''H''|tex}}|$$}}

yields the display style LaTeX

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

Tests

The code

: <math>\int_{0}^{1} x^3 dx</math> 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!)

$\int _{0}^{1}x^{3}dx$ and${\begin{array}{l}\displaystyle {\int _{0}^{1}x^{3}dx}\end{array}}$

The code

: <math>\Gamma(z) = \int_{0}^{\infty} e^{-t} t^{z-1} dt</math> 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!)

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