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Template:Integral/int

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alt = This template is under construction...
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! Green tickY)
(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 3dx
and 
1
0
x 3dx
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 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

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 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

\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<!--
-->{{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, ,  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
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

, , 

\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 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

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!)

and

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!)

and