Template:Integral/nicer/doc

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

[⧼Purge⧽ Template:Integral/nicer/doc]

This template is under construction.

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

The following code (which produces nicer integral symbols) requires
font-family: 'Lucida Sans Unicode';
which we cannot rely on being installed on the user’s computer/tablet/smartphone...

See also: {{integral}}, which produces not as nice integral symbols but DOES NOT require font-family: 'Lucida Sans Unicode'; which we cannot rely on being installed on the user’s computer/tablet/smartphone...

The {{integral/nicer}} mathematical formatting template is used to obtain an HTML+CSS or a $L a T e X$ formatted integral expression of one of the following types:

simple integral,
double integral,
triple integral,
quadruple integral,
multiple integral,
contour integral,
clockwise contour integral,
counterclockwise contour integral,
boundary surface integral,
boundary hypersurface integral.

Note: The {{integral/nicer}} template uses the {{integral/nicer/int}} helper template to implement the int (simple integral) option, which is also used to implement the iiiint (quadruple integral), and idotsint (multiple integral) options (since font-family: 'Lucida Sans Unicode'; does not support neither the quadruple integral symbol, nor the multiple integral symbol).

Usage

{{integral/nicer|type|from|to|integrand}}

or

{{integral/nicer|type|from|to|integrand|format}}

or

{{integral/nicer|type|from|to}} integrand

or

{{integral/nicer|type|from|to|format}} integrand

where the first argument (type) is from

**HTML+CSS integral symbols with `font-family: 'Lucida Sans Unicode';` rendered using the `{{math}}` template.**
*Note that* `font-family: 'Lucida Sans Unicode';` *does not support the quadruple integral symbol.*
*Integral symbols for text style (top two rows, italic for second row), and for display style (bottom two rows, italic for second row).*
∫	∬	∭	⨌	∮	∲	∳	∯	∰
∫	∬	∭	⨌	∮	∲	∳	∯	∰
`int`	`iint`	`iiint`	`iiiint`	`oint`	`varointclockwise`	`ointctrclockwise`	`oiint`	`oiiint`
∫	∬	∭	⨌	∮	∲	∳	∯	∰
∫	∬	∭	⨌	∮	∲	∳	∯	∰

**$L a T e X$ integral symbols rendered using the `{{math}}` template.**
*Integral symbols for text style (top two rows,* `\mathit{...}` *for second row), and for display style (bottom two rows,* `\mathit{...}` *for second row).*
*Package* `amsmath` *is used for double/triple/quadruple integrals.*
*Package* `esint` *is used for [closed] oriented path integrals and [closed] boundary double/triple integrals.*
$\textstyle {\int }$	$\textstyle {\iint }$	$\textstyle {\iiint }$	$\textstyle {\iiiint }$	$\textstyle {\oint }$	$\textstyle {\varointclockwise }$	$\textstyle {\ointctrclockwise }$	$\textstyle {\oiint }$	$\textstyle {\oiiint }$
$\textstyle {\mathit {\int }}$	$\textstyle {\mathit {\iint }}$	$\textstyle {\mathit {\iiint }}$	$\textstyle {\mathit {\iiiint }}$	$\textstyle {\mathit {\oint }}$	$\textstyle {\mathit {\varointclockwise }}$	$\textstyle {\mathit {\ointctrclockwise }}$	$\textstyle {\mathit {\oiint }}$	$\textstyle {\mathit {\oiiint }}$
`int`	`iint`	`iiint`	`iiiint`	`oint`	`varointclockwise`	`ointctrclockwise`	`oiint`	`oiiint`
${\begin{array}{l}\displaystyle {\int }\end{array}}$	${\begin{array}{l}\displaystyle {\iint }\end{array}}$	${\begin{array}{l}\displaystyle {\iiint }\end{array}}$	${\begin{array}{l}\displaystyle {\iiiint }\end{array}}$	${\begin{array}{l}\displaystyle {\oint }\end{array}}$	${\begin{array}{l}\displaystyle {\varointclockwise }\end{array}}$	${\begin{array}{l}\displaystyle {\ointctrclockwise }\end{array}}$	${\begin{array}{l}\displaystyle {\oiint }\end{array}}$	${\begin{array}{l}\displaystyle {\oiiint }\end{array}}$
${\begin{array}{l}\displaystyle {\mathit {\int }}\end{array}}$	${\begin{array}{l}\displaystyle {\mathit {\iint }}\end{array}}$	${\begin{array}{l}\displaystyle {\mathit {\iiint }}\end{array}}$	${\begin{array}{l}\displaystyle {\mathit {\iiiint }}\end{array}}$	${\begin{array}{l}\displaystyle {\mathit {\oint }}\end{array}}$	${\begin{array}{l}\displaystyle {\mathit {\varointclockwise }}\end{array}}$	${\begin{array}{l}\displaystyle {\mathit {\ointctrclockwise }}\end{array}}$	${\begin{array}{l}\displaystyle {\mathit {\oiint }}\end{array}}$	${\begin{array}{l}\displaystyle {\mathit {\oiiint }}\end{array}}$

Setting the background color [of a container span] to white (for testing purposes).

with description (these match the $L a T e X$ definitions exactly)

int: simple integral 
∫
∫,
iint: double integral 
∬
∬,
iiint: triple integral 
∭
∭,
iiiint: quadruple integral 
∫∫∫∫
∫∫∫∫ (instead of 
⨌
⨌),
idotsint: multiple integral 
∫⋯∫
∫ ⋯ ∫,
oint: [closed] path integral 
∮
∮,
varointclockwise: [closed] clockwise path integral 
∲
∲,
ointctrclockwise: [closed] counterclockwise path integral 
∳
∳,
oiint: [closed] boundary surface integral 
∯
∯,
oiiint: [closed] boundary hypersurface integral 
∰
∰;

and where

the second (from) and third (to) arguments are the limits of a definite integral;

and where

the fourth argument (integrand) is the mathematical expression to integrate (optional);

and where the fifth argument, or fourth argument if integrand is omitted, (format) is from

htm: HTML+CSS markup (text style) for integral expression (default),
HTM: HTML+CSS markup (display style) for integral expression,
tex: $L a T e X$ markup (text style) for integral expression,
TEX: $L a T e X$ markup (display style) for integral expression.

Examples

See also {{integral/testcases}} for more examples and/or tests.

Text style inline formulae

The code

: {{Wikipedia|Lorem ipsum|}} dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Gauss{{'}}s Law: {{math|
''{{Gr|epsilon}}''{{sub|0}}{{sp|3}}<!--
-->{{integral/nicer|oiint|{{d|{{Gr|Omega}}|part}}|<!--
-->|{{vec|E|b}}{{sp|1}}{{op|sdot}}{{sp|1}}{{d|{{sp|1}}{{vec|S|b}}}}<!--
-->}}<!--
--> {{=}} <!--
-->{{integral/nicer|iiint|{{Gr|Omega}}|<!--
-->|''{{Gr|rho}}''{{sp|3}}{{d|''V''}}<!--
-->}}
|&}}. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. {{math|
{{Gr|Gamma}}(''z'') {{=}} <!--
-->{{integral/nicer|int|0|infty
   |''e''{{^|{{op|-}}{{sp|1}}''t''}}{{sp|2}}''t''{{sp|2}}{{^|''z''{{sp|1}}{{op|-}}1}}{{sp|3}}{{d|''t''}}
   }}
|&}}. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

yields the HTML+CSS: Line spacing is undisturbed.

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Gauss’s Law: 

ϵ0

∯

∂ Ω

 E ⋅ d S =

∭

Ω

 ρ d V

. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. 

Γ(z) =

∫

∞

0

 e − t t z − 1 d t

. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

Examples without integrand as argument (as in $L a T e X$ )

The code

: {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|{{integral/nicer|int|''a''|''b''}} ''x''{{^|2}}{{sp|3}}{{d|''x''}} {{=}} {{tfrac|''b''{{^|3}} {{op|-}} ''a''{{^|3}}|3}}|&}} 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 

∫

b

a

  x 2 d x =

b 3 − a 3

3

after
yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda

The code

: {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|{{integral/nicer|int|''a''|''b''|tex}} ''x''{{^|2|tex}}{{sp|3|tex}}{{d|''x''|tex}} {{=}} {{tfrac|''b''{{^|3|tex}} {{op|-}} ''a''{{^|3|tex}}|3|tex}}|$}} after{{repeat|2|{{nl}}{{repeat|5|yadda{{nbsp}}}}}}

yields the text style $L a T e X$

yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda
before

\textstyle {\int _{a}^{b}\;x^{2}{\,}d^{}x={\tfrac {b^{3}{\,}-{\,}a^{3}}{3}}}

after
yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda

The code

{{indent}}{{math|{{integral/nicer|int|''a''|''b''|HTM}} ''x''{{^|2}}{{sp|3}}{{d|''x''}} {{=}} {{frac|''b''{{^|3}} {{op|-}} ''a''{{^|3}}|3|HTM}}|&&}}

yields the display style HTML+CSS

∫

b

a

x 2 d x =

b 3 − a 3

3

The code

{{indent}}{{math|{{integral/nicer|int|''a''|''b''|TEX}} ''x''{{^|2|tex}}{{sp|3|tex}}{{d|''x''|tex}} {{=}} {{frac|''b''{{^|3|tex}} {{op|-}} ''a''{{^|3|tex}}|3|TEX}}|$$}}

yields the display style $L a T e X$

${\begin{array}{l}\displaystyle {\int _{a}^{b}\;x^{2}{\,}d^{}x={\frac {b^{3}-a^{3}}{3}}}\end{array}}$

Examples with integrand as argument

The code

: {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|{{integral/nicer|int|''a''|''b''|''x''{{^|2}}{{sp|3}}{{d|''x''}}}} {{=}} {{tfrac|''b''{{^|3}} {{op|-}} ''a''{{^|3}}|3}}|&}} 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 

∫

b

a

 x 2 d x =

b 3 − a 3

3

after
yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda

The code

: {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|{{integral/nicer|int|''a''|''b''|''x''{{^|2|tex}}{{sp|3|tex}}{{d|''x''|tex}}|tex}} {{=}} {{tfrac|''b''{{^|3|tex}} {{op|-}} ''a''{{^|3|tex}}|3|tex}}|$}} after{{repeat|2|{{nl}}{{repeat|5|yadda{{nbsp}}}}}}

yields the text style $L a T e X$

yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda
before

\textstyle {\int _{a}^{b}\;{x^{2}{\,}d^{}x}={\tfrac {b^{3}{\,}-{\,}a^{3}}{3}}}

after
yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda

The code

{{indent}}{{math|{{integral/nicer|int|''a''|''b''|''x''{{^|2}}{{sp|3}}{{d|''x''}}|HTM}} {{=}} {{frac|''b''{{^|3}} {{op|-}} ''a''{{^|3}}|3|HTM}}|&&}}

yields the display style HTML+CSS

∫

b

a

 x 2 d x =

b 3 − a 3

3

The code

{{indent}}{{math|{{integral/nicer|int|''a''|''b''|''x''{{^|2|tex}}{{sp|3|tex}}{{d|''x''|tex}}|TEX}} {{=}} {{frac|''b''{{^|3|tex}} {{op|-}} ''a''{{^|3|tex}}|3|TEX}}|$$}}

yields the display style $L a T e X$

${\begin{array}{l}\displaystyle {\int _{a}^{b}\;{x^{2}{\,}d^{}x}={\frac {b^{3}-a^{3}}{3}}}\end{array}}$

Gamma function

The code

: {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|{{Gr|Gamma}}(''z'') {{=}} {{integral/nicer|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|{{Gr|Gamma|tex}}(''z'') {{=}} {{integral/nicer|int|0|infty|''e''{{^|{{op|-}}{{sp|1|tex}}''t''|tex}}{{sp|2|tex}}''t''{{^|{{sp|1|tex}}''z''{{op|-}}1|tex}}{{sp|3|tex}}{{d|''t''|tex}}|tex}}|$}} after{{repeat|2|{{nl}}{{repeat|5|yadda{{nbsp}}}}}}

yields the text style $L a T e X$

yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda
before

\textstyle {\Gamma (z)=\int _{0}^{\infty }\;{e^{{\,}-{\,}{\;\;\!\!\!}t}{\;\!}t^{{\;\;\!\!\!}z{\,}-{\,}1}{\,}d^{}t}}

after
yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda

The code

{{indent}}{{math|{{Gr|Gamma}}(''z'') {{=}} {{integral/nicer|int|0|infty|''e''{{^|{{op|-}}{{sp|1}}''t''}}{{sp|2}}''t''{{^|{{sp|2}}''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

{{indent}}{{math|{{Gr|Gamma|tex}}(''z'') {{=}} {{integral/nicer|int|0|infty|''e''{{^|{{op|-}}{{sp|1|tex}}''t''|tex}}{{sp|2|tex}}''t''{{^|{{sp|1|tex}}''z''{{op|-}}1|tex}}{{sp|3|tex}}{{d|''t''|tex}}|TEX}}|$$}}

yields the display style $L a T e X$

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

Contour integrals and boundary integrals

The code

: {{repeat|2|{{repeat|7|yadda{{nbsp}}}}{{nl}}}}before {{math|
{{integral/nicer|varointclockwise|''C''||''F''{{sp|1}}({{vec|x|b}}){{sp|1}}{{op|sdot}}{{sp|1}}{{d|{{vec|x|b}}}}}} {{=}} <!--
  -->{{op|-}}{{sp|1}}{{integral/nicer|ointctrclockwise|''C''||''F''{{sp|1}}({{vec|x|b}}){{sp|1}}{{op|sdot}}{{sp|1}}{{d|{{vec|x|b}}}}}}
|tex = {{integral/nicer|varointclockwise|C||F({{vec|x|b|tex}}) \sdot {{d|{{vec|x|b|tex}}|tex}}|tex}} {{=}} <!--
  -->- {{integral/nicer|ointctrclockwise|C||F({{vec|x|b|tex}}) \sdot {{d|{{vec|x|b|tex}}|tex}}|tex}} 
|&}} after{{repeat|2|{{nl}}{{repeat|7|yadda{{nbsp}}}}}}

yields the text style HTML+CSS

yadda yadda yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda yadda yadda
before

∲

C

 F (x) ⋅ d x = −

∳

C

 F (x) ⋅ d x

after
yadda yadda yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda yadda yadda

and with the $ option, yields the display style $L a T e X$

yadda yadda yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda yadda yadda
before

\textstyle {{\mathit {\varointclockwise }}\!_{C}^{}\;{F(\mathbf {x} )\cdot d^{}\mathbf {x} }=-{\mathit {\ointctrclockwise }}\!_{C}^{}\;{F(\mathbf {x} )\cdot d^{}\mathbf {x} }}

after
yadda yadda yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda yadda yadda

The code

{{indent}}{{math|
{{integral/nicer|varointclockwise|''C''||''F''{{sp|1}}({{vec|x|b}}){{sp|1}}{{op|sdot}}{{sp|1}}{{d|{{vec|x|b}}}}|HTM}} {{=}} <!--
  -->{{op|-}}{{sp|1}}{{integral/nicer|ointctrclockwise|''C''||''F''{{sp|1}}({{vec|x|b}}){{sp|1}}{{op|sdot}}{{sp|1}}{{d|{{vec|x|b}}}}|HTM}}
|tex = {{integral/nicer|varointclockwise|C||F({{vec|x|b|tex}}) \sdot {{d|{{vec|x|b|tex}}|tex}}|TEX}} {{=}} <!--
  -->- {{integral/nicer|ointctrclockwise|C||F({{vec|x|b|tex}}) \sdot {{d|{{vec|x|b|tex}}|tex}}|TEX}}
|&&}}

yields the display style HTML+CSS

∲

C

 F (x) ⋅ d x = −

∳

C

 F (x) ⋅ d x

and with the $$ option, yields the display style $L a T e X$

${\begin{array}{l}\displaystyle {{\mathit {\varointclockwise }}\!_{C}^{}\;{F(\mathbf {x} )\cdot d^{}\mathbf {x} }=-{\mathit {\ointctrclockwise }}\!_{C}^{}\;{F(\mathbf {x} )\cdot d^{}\mathbf {x} }}\end{array}}$

Maxwell's equations

The code

{{indent}}{{math|
{{align|begin}}
{{integral/nicer|oiint|{{d|''V''|part}}||{{vec|E|b}}{{sp|1}}{{op|sdot}}{{sp|1}}{{d|{{vec|S|b}}}}|HTM}} {{&=}} <!--
  -->{{frac|1|''{{Gr|epsilon}}''{{sub|0}}}} {{integral/nicer|iiint|''V''||''{{Gr|rho}}''{{sp|3}}{{d|''V''}}|HTM}} {{\\}}

{{integral/nicer|oiint|{{d|''V''|part}}||{{vec|B|b}}{{sp|1}}{{op|sdot}}{{sp|1}}{{d|{{vec|S|b}}}}|HTM}} {{&=}} 0 {{\\}}

{{integral/nicer|oint|{{d|''S''|part}}||{{vec|E|b}}{{sp|1}}{{op|sdot}}{{sp|1}}{{d|{{vec|x|b}}}}|HTM}} {{&=}} <!--
  -->{{op|−}}{{integral/nicer|iint|''S''||{{partial|{{vec|B|b}}|''t''}}{{sp|1}}{{op|sdot}}{{sp|1}}{{d|{{vec|S|b}}}}|HTM}} {{\\}}

{{integral/nicer|oint|{{sym|partial}}''S''||{{vec|B|b}}{{sp|1}}{{op|sdot}}{{sp|1}}{{d|{{vec|x|b}}}}|HTM}} {{&=}} <!--
  -->{{integral/nicer|iint|''S''||{{(|''{{Gr|mu}}''{{sub|0}}{{sp|1}}{{vec|J|b}} + {{frac|1|''c''{{^|2}}}} <!--
  -->{{partial|{{vec|E|b}}|''t''}}|)|Big}}{{sp|1}}{{op|sdot}}{{sp|1}}{{d|{{vec|S|b}}}}|HTM}}
{{align|end}}
|&&}}

yields the display style HTML+CSS

Error: String exceeds 10,000 character limit.

The code

{{indent}}{{math|
{{align|begin|tex}}
{{integral/nicer|oiint|{{d|V|part|tex}}||{{vec|E|b|tex}} \sdot {{d|{{vec|S|b|tex}}|tex}}|TEX}} {{&=|tex}} <!--
  -->\frac{1}{\epsilon_0} {{integral/nicer|iiint|V||\rho \, {{d|V|tex}}|TEX}} {{\\|tex}}

{{integral/nicer|oiint|{{d|V|part|tex}}||{{vec|B|b|tex}} \sdot {{d|{{vec|S|b|tex}}|tex}}|TEX}} {{&=|tex}} 0 {{\\|tex}}

{{integral/nicer|oint|{{d|S|part|tex}}||{{vec|E|b|tex}} \sdot {{d|{{vec|x|b|tex}}|tex}}|TEX}} {{&=|tex}} <!--
  -->- {{iint|S||{{partial|{{vec|B|b|tex}}|t|TEX}} \sdot {{d|{{vec|S|b|tex}}|tex}}|TEX}} {{\\|tex}} 

{{integral/nicer|oint|{{d|S|part|tex}}||{{vec|B|b|tex}} \sdot {{d|{{vec|x|b|tex}}|tex}}|TEX}} {{&=|tex}} <!--
  -->{{integral/nicer|iint|S||{{(|\mu_0 \, {{vec|J|b|tex}} + \frac{1}{c^2} <!--
  -->{{partial|{{vec|E|b|tex}}|t|TEX}}|)|Big|tex}} \sdot {{d|{{vec|S|b|tex}}|tex}}|TEX}}
{{align|end|tex}}
|$$}}

yields the display style $L a T e X$

${\begin{array}{l}\displaystyle {\begin{aligned}{\mathit {\oiint }}\!_{\,{\partial }^{}V}^{}\;{\mathbf {E} \cdot d^{}\mathbf {S} }&={\frac {1}{\epsilon _{0}}}\iiint _{V}^{}\;{\rho \,d^{}V}\\{\mathit {\oiint }}\!_{\,{\partial }^{}V}^{}\;{\mathbf {B} \cdot d^{}\mathbf {S} }&=0\\\oint _{\,{\partial }^{}S}^{}\;{\mathbf {E} \cdot d^{}\mathbf {x} }&=-\iint _{S}^{}\;{{\dfrac {{\partial }^{}\mathbf {B} }{{\partial }{t}^{}}}\cdot d^{}\mathbf {S} }\\\oint _{\,{\partial }^{}S}^{}\;{\mathbf {B} \cdot d^{}\mathbf {x} }&=\iint _{S}^{}\;{{\Big (}\mu _{0}\,\mathbf {J} +{\frac {1}{c^{2}}}{\dfrac {{\partial }^{}\mathbf {E} }{{\partial }{t}^{}}}{\Big )}\cdot d^{}\mathbf {S} }\end{aligned}}\end{array}}$

`\iint` and `\iiint` and `\iiiint`

The code

: {{repeat|2|{{repeat|10|yadda{{nbsp}}}}{{nl}}}}<!--
-->before {{math|''F'' {{=}} {{integral/nicer|iint|2-ball}} {{d|''F''}},{{sp|quad}}''G'' {{=}} {{integral/nicer|iiint|3-ball}} {{d|''G''}},{{sp|quad}}''H'' {{=}} {{integral/nicer|iiiint|4-ball}} {{d|''H''}}
|tex = F = {{integral/nicer|iint|2-ball||tex}} {{d|F|tex}},\quad G = {{integral/nicer|iiint|3-ball||tex}} {{d|G|tex}},\quad H = {{integral/nicer|iiiint|4-ball||tex}} {{d|H|tex}}|&}} 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

  d F, G =

∭

3-ball

  d G, H =

∫

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'' {{=}} {{integral/nicer|iint|2-ball|}} {{d|''F''}},{{sp|quad}}''G'' {{=}} {{integral/nicer|iiint|3-ball|}} {{d|''G''}},{{sp|quad}}''H'' {{=}} {{integral/nicer|iiiint|4-ball|}} {{d|''H''}}
|tex = F = {{integral/nicer|iint|2-ball||tex}} {{d|F|tex}},\quad G = {{integral/nicer|iiint|3-ball||tex}} {{d|G|tex}},\quad H = {{integral/nicer|iiiint|4-ball||tex}} {{d|H|tex}}|$}} after<!--
-->{{repeat|2|{{nl}}{{repeat|10|yadda{{nbsp}}}}}}

yields the text style $L a T e X$

yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda yadda yadda yadda yadda yadda
before

\textstyle {F=\iint _{2-ball}^{}\;d^{}F,\quad G=\iiint _{3-ball}^{}\;d^{}G,\quad H=\iiiint _{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

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

yields the display style HTML+CSS

F =

∬

2-ball

d F, G =

∭

3-ball

d G, H =

∫

4-ball

d H

The code

: {{math|''F'' {{=}} {{integral/nicer|iint|2-ball||HTM}} {{d|''F''}},{{sp|quad}}''G'' {{=}} {{integral/nicer|iiint|3-ball||HTM}} {{d|''G''}},{{sp|quad}}''H'' {{=}} {{integral/nicer|iiiint|4-ball||HTM}} {{d|''H''}}
|tex = F = {{integral/nicer|iint|2-ball||TEX}} {{d|F|tex}},\quad G = {{integral/nicer|iiint|3-ball||TEX}} {{d|G|tex}},\quad H = {{integral/nicer|iiiint|4-ball||TEX}} {{d|H|tex}}|$$}}

yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {F=\iint _{2-ball}^{}\;d^{}F,\quad G=\iiint _{3-ball}^{}\;d^{}G,\quad H=\iiiint _{4-ball}^{}\;d^{}H}\end{array}}

`\idotsint`

The code

: {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|''H'' {{=}} {{integral/nicer|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

  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'' {{=}} {{integral/nicer|idotsint|''n''\text{-ball}||tex}} {{d|''H''|tex}}|$}} after{{repeat|2|{{nl}}{{repeat|5|yadda{{nbsp}}}}}}

yields the text style $L a T e X$

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'' {{=}} {{integral/nicer|idotsint|''n''-ball||HTM}} {{d|''H''}}|&&}}

yields the display style HTML+CSS

H =

∫

⋯

∫

n-ball

d H

The code

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

yields the display style $L a T e X$

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

Quotient of integrals

The code

: {{math|<!-- 
-->{{frac
   | {{integral/nicer|int|0|infty|''x''{{^|2{{sp|1}}''n''}}{{sp|1}}''e''{{^|{{op|-}}''a''{{sp|1}}''x''{{^|2}}}}{{sp|3}}{{d|''x''}}}}<!-- 
-->| {{integral/nicer|int|0|infty|''x''{{^|2{{sp|1}}(''n''{{sp|1}}{{op|-}}1)}}{{sp|1}}''e''{{^|{{op|-}}''a''{{sp|1}}''x''{{^|2}}}}{{sp|3}}{{d|''x''}}}}<!-- 
-->|HTM}} {{=}} {{frac|2{{sp|1}}''n'' {{op|-}} 1|2{{sp|1}}''a''|HTM}}
|tex = \frac{ \int_{0}^{\infty} x^{2n} e^{-a x^2} dx }{ \int_{0}^{\infty} x^{2(n-1)} e^{-a x^2} dx } = \frac{2n - 1}{2a} 
|&&}}

yields the display style HTML+CSS

∫

∞

0

 x 2 n e − a x 2 d x

∫

∞

0

 x 2 (n − 1) e − a x 2 d x

=

2 n − 1

2 a

and with the $$ option, yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {{\frac {\int _{0}^{\infty }x^{2n}e^{-ax^{2}}dx}{\int _{0}^{\infty }x^{2(n-1)}e^{-ax^{2}}dx}}={\frac {2n-1}{2a}}}\end{array}}

The code

: {{math|<!-- 
-->{{frac
   | {{integral/nicer|oiint|{{sym|partial}}{{sp|1}}{{Gr|Omega}}| |{{vec|E|b}}{{op|sdot}}{{d|{{vec|S|b}}}}}}<!-- 
-->| {{integral/nicer|iiint|{{Gr|Omega}}| |''{{Gr|rho}}''{{sp|3}}{{d|''V''}}}}<!-- 
-->|HTM}} {{=}} {{frac|1|''{{Gr|epsilon}}''{{sub|0}}|HTM}}
|tex = <!-- 
-->{{frac
   | {{integral/nicer|oiint|{{sym|partial|tex}}{{Gr|Omega|tex}}| |{{vec|E|b|tex}}{{op|sdot|tex}}{{d|{{vec|S|b|tex}}|tex}}|tex}}<!-- 
-->| {{integral/nicer|iiint|{{Gr|Omega|tex}}| |''{{Gr|rho|tex}}''{{sp|3|tex}}{{d|''V''|tex}}|tex}}<!-- 
-->|TEX}} {{=}} {{frac|1|''{{Gr|epsilon|tex}}''{{sub|0|tex}}|TEX}}
|&&}}

yields the display style HTML+CSS

∯

∂ Ω

 E ⋅ d S

∭

Ω

 ρ d V

=

1

ϵ0

and with the $$ option, yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {{\frac {{\mathit {\oiint }}\!_{{\partial }\Omega }^{}\;{\mathbf {E} {\;\!}{\cdot }{\;\!}d^{}\mathbf {S} }}{\iiint _{\Omega }^{}\;{\rho {\,}d^{}V}}}={\frac {1}{\epsilon _{0}{\!\,\!}}}}\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 $L a T e X$ (Not the fault of the {{math}} template: MS Edge chops $L a T e X$ 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 $L a T e X$ (Not the fault of the {{math}} template: MS Edge chops $L a T e X$ 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}}

Tests for new code

The code

: {{repeat|2|{{repeat|5|yadda{{nbsp}}}}{{nl}}}}before {{math|<!-- text style HTML+CSS (default)
--><table class{{=}}"@middle@" cellpadding{{=}}"0" cellspacing{{=}}"0" 
    style{{=}}"display: inline-table; vertical-align: middle; font-size: 1.25em; text-align: left; border: 0; border-collapse: collapse; margin: -1.55ex 0 -1.45ex 0.1em; padding: 0;"><!--
    Invisible table for the integral symbol and sub-table for text style limits (as subscript and superscript of the integral symbol) 
    --><tr><!-- 
      --><td><span style{{=}}"vertical-align: 0.6ex; margin: 0 -0.1ex 0 -0.3ex; font-family: 'Lucida Sans Unicode';"><!--
      -->''{{#switch: <!--{{{1|int}}}-->iint | iint = ∬ | iiint = ∭ | iiiint = ⨌ | oint = ∮ | varointclockwise = ∲ | ointctrclockwise = ∳ | oiint = ∯ | oiiint = ∰ }}''<!--
      --></span></td><!-- 
      --><td><table cellpadding{{=}}"0" cellspacing{{=}}"0" style{{=}}"display: inline-table; border: 0; border-collapse: collapse; margin: -2.5ex 0 -1.0ex 0; padding: 0; padding: 0;"><!-- sub-table for limits of the integral
        --><tr><td style{{=}}"text-align: left;"><span style{{=}}"vertical-align: 0.8ex; margin-left: 0.25em; padding: 0; font-size: 0.6em; line-height: 0.4em; visibility: {{#if: <!--{{{3|}}}--> |visible|hidden}};"><!-- upper limit as superscript
        -->{{#replace: {{#replace: {{#replace: {{#if: <!--{{{3|}}}--> |<!--{{{3}}}-->|<!--{{{2|}}}-->''D''<!-- hidden -->}}
                                   |@opsp@|{{sp|1}}}}
                       |infty| ∞}}<!--
        -->| ∞|<span style{{=}}"font-size: 1.15em;">∞<!--  ∞ --></span>}}<!--
        --></span></td></tr><!--
        --><tr><td style{{=}}"text-align: left;"><span style{{=}}"vertical-align: 2.0ex; margin: 0 0 -1.5ex -0.1em; padding: 0; font-size: 0.6em; line-height: 0.4em;"><!-- lower limit as subscript 
        -->{{#replace: {{#replace: {{#replace: {{#if: <!--{{{2|}}}-->''D'' |<!--{{{2}}}-->''D''|{{sp|1}}}}
                                   |@opsp@|{{sp|1}}}}
                       |infty| ∞}}<!--
        -->| ∞|<span style{{=}}"font-size: 1.15em;">∞<!--  ∞ --></span>}}<!--
        --></span></td></tr><!--
      --></table></td><!--
    --></tr><!--
  --></table> ''f''{{sp|2}}(''x'', ''y''){{sp|3}}{{d|''x''}}{{sp|3}}{{d|''y''}}|&}} 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 

∬

D

f (x, y) d x d y

after
yadda yadda yadda yadda yadda
yadda yadda yadda yadda yadda

External links

Template:Intorient—Wikipedia.org.

{{sum}} (summation)
{{prod}} (product)

Template:Integral/nicer/doc

Contents

Usage

Examples

Text style inline formulae

Examples without integrand as argument (as in $L a T e X$ )

Examples with integrand as argument

Gamma function

Contour integrals and boundary integrals

Maxwell's equations

`\iint` and `\iiint` and `\iiiint`

`\idotsint`

Quotient of integrals

Tests

Tests for new code

See also

External links

Navigation menu

Views

Personal tools

Navigation

Search

Tools

Template:Integral/nicer/doc

Contents

Usage

Examples

Text style inline formulae

Examples without integrand as argument (as in LaTeX)

Examples with integrand as argument

Gamma function

Contour integrals and boundary integrals

Maxwell's equations

\iint and \iiint and \iiiint

\idotsint

Quotient of integrals

Tests

Tests for new code

See also

External links

Navigation menu

Search

Examples without integrand as argument (as in $L a T e X$ )

`\iint` and `\iiint` and `\iiiint`

`\idotsint`