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| {{distinguish|Long s|Esh (letter)}}
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| The '''integral symbol''':
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| :<big><big><big>{{Unicode|∫}}</big></big></big> ([[Unicode]]), <math>\displaystyle \int</math> ([[LaTeX]])
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| is used to denote [[integral]]s and [[antiderivatives]] in [[mathematics]]. The notation was introduced by the [[Germany|German]] mathematician [[Gottfried Wilhelm Leibniz]] towards the end of the 17th century. The symbol was based on the {{Unicode|ſ}} ([[long s]]) character, and was chosen because Leibniz thought of the integral as an infinite [[summation|sum]] of infinitesimal [[summand]]s. See [[long s]] for more details on the history of {{Unicode|ſ}}. | |
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| == Typography in Unicode and LaTeX ==
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| ===Fundamental symbol===
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| {{main|Integral calculus}}
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| The integral symbol is {{unichar|222B|INTEGRAL}} in [[Unicode]]<ref name="Unicode Mathematical Operators">{{cite web| title = Mathematical Operators – Unicode| url = http://www.unicode.org/charts/PDF/U2200.pdf| accessdate = 2013-04-26}}</ref> and <code>\int</code> in [[LaTeX]]. In [[HTML]], it is written as <code>&#x222b;</code> ([[hexadecimal]]), <code>&#8747;</code> ([[decimal]]) and <code>&int;</code> (named "entity").
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| The original [[IBM PC]] [[code page 437]] character set included a couple of characters {{Unicode|⌠}} and {{Unicode|⌡}} (codes 244 and 245, respectively) to build the integral symbol. These were deprecated in subsequent [[MS-DOS]] [[code page]]s, but they still remain in [[Unicode]] (U+2320 and U+2321, respectively) for compatibility.
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| The {{Unicode|∫}} symbol is very similar to, but not to be confused with, the [[ʃ]] symbol (called "[[esh (letter)|esh]]").
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| ===Extensions of the symbol===
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| {{see also|Multiple integral}}
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| Related symbols include:<ref name="Unicode Mathematical Operators"/><ref name="Unicode Supplemental Mathematical Operators">{{cite web| title = Supplemental Mathematical Operators – Unicode| url = http://www.unicode.org/charts/PDF/U2A00.pdf| accessdate = 2013-05-05}}</ref>
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| :{| class="wikitable"
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| |-
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| ! Meaning
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| ! scope="col" colspan="2"| [[Unicode]]
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| ! scope="col" colspan="2"| [[LaTeX]]
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| |-
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| ! [[Double integral]]
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| |style="font-size:20pt;"| {{Unicode|∬}}
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| || U+222C
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| || <math>\iint</math>
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| || <code>\iint</code>
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| |-
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| ! [[Triple integral]]
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| |style="font-size:20pt;"| {{Unicode|∭}}
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| || U+222D
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| || <math>\iiint</math>
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| || <code>\iiint</code>
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| |-
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| ! [[Contour integral]]
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| |style="font-size:20pt;"| {{Unicode|∮}}
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| || U+222E
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| || <math>\oint</math>
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| || <code>\oint</code>
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| |-
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| ! [[Clockwise]] integral
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| |style="font-size:20pt;"| {{Unicode|∱}}
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| || U+2231
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| |-
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| ! [[Anticlockwise]] integral
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| |style="font-size:20pt;"| {{Unicode|⨑}}
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| || U+2A11
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| |-
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| ! Clockwise contour integral
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| |style="font-size:20pt;"| {{Unicode|∲}}
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| || U+2232
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| || {{Intorient|symbol=varoint}}
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| || <code>\varointclockwise</code>
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| |-
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| ! Anticlockwise contour integral
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| |style="font-size:20pt;"| {{Unicode|∳}}
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| || U+2233
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| || {{Intorient|symbol=ointctr}}
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| || <code>\ointctrclockwise</code>
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| |-
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| ! [[closed manifold|Closed]] [[surface integral]]
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| |style="font-size:20pt;"| {{Unicode|∯}}
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| || U+222F
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| || {{oiint}}
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| || <code>\oiint</code>
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| ! Closed [[volume integral]]
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| |style="font-size:20pt;"| {{Unicode|∰}}
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| || U+2230
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| || {{oiiint}}
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| || <code>\oiiint</code>
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| |-
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| |}
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| == Typography in other languages ==
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| [[File:Integral Uprightness.svg|150px|thumb|Regional variations (English, German, Russian) of the integral symbol.]]
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| In other languages, the shape of the integral symbol differs slightly from the shape commonly seen in English-language textbooks. While the [[English language|English]] integral symbol leans to the right, the [[German language|German]] symbol (used throughout [[Central Europe]]) is upright, and the [[Russian language|Russian]] variant leans to the left.
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| Another difference is in the placement of [[limits of integration|limits]] for [[definite integral]]s. Generally, in English-language books, limits go to the right of the integral symbol: <math> \int_0^T f(t)\;dt </math>.
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| By contrast, in German and Russian texts, [[limits of integration|limits]] for [[definite integral]]s are placed above and below the integral symbol, and, as a result, the notation requires larger line spacing: <math> \int\limits_0^T f(t)\;\mathrm{d}t </math>.
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| == See also ==
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| * [[Capital sigma notation]]
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| * [[Capital pi notation]]
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| == Notes ==
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| {{Reflist}}
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| == References==
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| *{{cite book | last = Stewart | first = James | title = Single Variable Calculus: Early Transcendentals | accessdate = 2006-06-26 | edition = 5th edition | year = 2003 | publisher = Brooks/Cole | location = [[Belmont, California|Belmont, CA]] | isbn = 0-534-39330-6 | chapter = Integrals | page = 381}}
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| *{{citation | last1 = Zaitcev | first1 = V. | last2 = Janishewsky | first2 = A. | last3 = Berdnikov | first3 = A. | contribution = Russian Typographical Traditions in Mathematical Literature | contribution-url = http://www.uni-giessen.de/partosch/eurotex99/zaitsev.pdf | series = EuroTeX'99 Proceedings | year = 1999}}
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| == External links ==
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| * [http://www.fileformat.info/info/unicode/char/222b/index.htm Fileformat.info]
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| {{Infinitesimals}}
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| [[Category:History of calculus]]
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| [[Category:Mathematical symbols]]
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Wilber Berryhill is the name his mothers and fathers gave him and he totally accurate psychic predictions (experienced) digs that title. The favorite pastime for him and his kids is to play lacross and he would never give it up. Some time in the past he chose to reside in North Carolina and he doesn't strategy on altering it. Credit authorising is exactly where my main earnings comes from.
my blog - psychic tarot card readings, http://Appin.co.kr/, readings (http://help.ksu.edu.sa/node/65129)