Integral sign
∫



Mathematical signs  
arithmetic  
Plus sign  + 
Minus sign   , ./. 
Mark  ⋅ , × 
Divided sign  : , ÷ , / 
Plus minus sign  ± , ∓ 
Comparison sign  < , ≤ , = , ≥ , > 
Root sign  √ 
Percent sign  % 
Analysis  
Sum symbol  Σ 
Product mark  Π 
Difference sign , Nabla  ∆ , ∇ 
Prime  ′ 
Partial differential  ∂ 
Integral sign  ∫ 
Concatenation characters  ∘ 
Infinity symbol  ∞ 
geometry  
Angle sign  ∠ , ∡ , ∢ , ∟ 
Vertical , parallel  ⊥ , ∥ 
Triangle , square  △ , □ 
Diameter sign  ⌀ 
Set theory  
Union , cut  ∪ , ∩ 
Difference , complement  ∖ , ∁ 
Element character  ∈ 
Subset , superset  ⊂ , ⊆ , ⊇ , ⊃ 
Empty set  ∅ 
logic  
Follow arrow  ⇒ , ⇔ , ⇐ 
Universal quantifier  ∀ 
Existential quantifier  ∃ 
Conjunction , disjunction  ∧ , ∨ 
Negation sign  ¬ 
The integral sign is derived from the letter s ("ſ") as an abbreviation for the word sum , Latin ſumma . This symbolic notation of integrals goes back to Gottfried Wilhelm Leibniz . For the integral sign there are a number of variations, including for multiple integrals , line integrals , surface integrals and volume integrals .
history
Leibniz first mentioned the integral sign in a later published manuscript Analysis tetragonistica of October 29, 1675.
" Utile erit scripsisse ∫ pro omnia "
"It will be useful to write ∫ instead of omnia"
Omnia stands for omnia l and is used in the geometrically oriented area calculationmethodby Bonaventura Cavalieri . Leibniz's corresponding printed publication is De geometria recondita ( Latin for “The geometry is saved”), from 1686. At that time he called the integral calculus calculus summatorius , hence the long S. Johann I Bernoulli was also busy at the time with the topic, and since Leibniz was striving for uniform scientific symbols, they discussed it. So the sign of Leibniz and the name calculus integralis , integral calculus, remained from Bernoulli.
use
The integral of a real function with respect to the variable over the interval is given by
written down. The multiplicative notation indicates how the integral operation from strips of height and infinitesimal width adds up to the area under the function.
Traditions of the formula set
Slightly different forms of the integral sign have become established in the various traditions of the formula set . In the German formula set, the form shown in the picture German form of the integral sign is used, while, for example, in the Russian area a form variant has been established that reproduces the graphic Russian form variant of the integral sign.
In addition, in American typesetting, the upper and lower limits are placed to the right of the integral sign in text formulas in order to limit disruptive line spacing.
while in German tradition
is common. Integrals in text formulas are always smaller than in separate formulas.
Coding
The integral symbol and its modifications are encoded in computer systems as follows.
character  Unicode  designation  HTML  Latex  

position  designation  hexadecimal  decimal  named  
∫ 
U+222B

integral  integral  & # x222B;  & # 8747;  & int; 
\int

∬ 
U+222C

double integral  Double integral  & # x222C;  & # 8748; 
\iint


∭ 
U+222D

triple integral  Triple integral  & # x222D;  & # 8749; 
\iiint


∮ 
U+222E

contour integral  Curve integral  & # x222E;  & # 8750; 
\oint


∯ 
U+222F

surface integral  Surface integral  & # x222F;  & # 8751; 
\oiint


∰ 
U+2230

volume integral  Volume integral  & # x2230;  & # 8752; 
\oiiint


∱ 
U+2231

clockwise integral  clockwise integral  & # x2231;  & # 8753; 
\intclockwise


∲ 
U+2232

clockwise contour integral  clockwise curve integral  & # x2232;  & # 8754; 
\ointclockwise


∳ 
U+2233

anticlockwise contour integral  counterclockwise curve integral  & # x2233;  & # 8755; 
\ointctrclockwise


⌠ 
U+2320

top half integral  upper half of an integral  & # x2320;  & # 8992;  
⌡ 
U+2321

bottom half integral  lower half of an integral  & # x2321;  & # 8993;  
⎮ 
U+23AE

integral extension  Extension of an integral  & # x23AE;  & # 9134;  
⨋ 
U+2A0B

summation with integral  Integral sum  & # x2A0B;  & # 10763; 
\sumint


⨌ 
U+2A0C

quadruple integral operator  Quadruple integral  & # x2A0C;  & # 10764; 
\iiiint


⨍ 
U+2A0D

finite part integral  Integral with finite part  & # x2A0D;  & # 10765; 
\dashint


⨎ 
U+2A0E

integral with double stroke  Integral with double line  & # x2A0E;  & # 10766; 
\ddashint


⨏ 
U+2A0F

integral average with slash  Mean value integral with dash  & # x2A0F;  & # 10767; 
\strokedint


⨑ 
U+2A11

anticlockwise integration  counterclockwise integral  & # x2A11;  & # 10769; 
\intctrclockwise


⨕ 
U+2A15

integral around a point operator  Integral around a point  & # x2A15;  & # 10773;  
⨖ 
U+2A16

quaternion integral operator  Quaternion integral  & # x2A16;  & # 10774; 
\sqint


⨗ 
U+2A17

integral with leftwards arrow with hook  Integral with left arrow with hook  & # x2A17;  & # 10775;  
⨘ 
U+2A18

integral with times sign  Integral with marks  & # x2A18;  & # 10776;  
⨙ 
U+2A19

integral with intersection  Integral with average  & # x2A19;  & # 10777; 
\landdownint


⨚ 
U+2A1A

integral with union  Integral with union  & # x2A1A;  & # 10778; 
\landupint


⨛ 
U+2A1B

integral with overbar  Integral with overline  & # x2A1B;  & # 10779;  
⨜ 
U+2A1C

integral with underbar  Integral with underscore  & # x2A1C;  & # 10780; 
Web links
Individual evidence
 ^ Carl von Prantl: Leibniz, Gottfried Wilhelm . In: Allgemeine Deutsche Biographie (ADB). Volume 18, Duncker & Humblot, Leipzig 1883, pp. 172209., Search calculus summatorius
 ^ Alfred Warner, Historical Dictionary of Electrical Engineering, Information Technology and Electrophysics
 ↑ Zaitcev, V .; Janishewsky, A .; Berdnikov, A. (1999), Russian Typographical Traditions in Mathematical Literature. EuroTeX'99 Proceedings ( Online ( Memento of the original from September 28, 2012 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this note .; PDF; 200 kB )
 ↑ Scott Pakin: The Comprehensive LaTeX Symbol List. (PDF, 8.7 MB) January 19, 2017, archived from the original on September 28, 2017 ; Retrieved on September 28, 2017 (English, linking the original results in a mirror of CTAN , the archive link compare file: Comprehensive LaTeX Symbol list.pdf ).