# 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
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 . ${\ displaystyle \ textstyle \ int}$

## 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 ${\ displaystyle f}$${\ displaystyle x}$ ${\ displaystyle [a, b]}$

${\ displaystyle \ int \ limits _ {a} ^ {b} f (x) \; \ mathrm {d} x}$

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. ${\ displaystyle f (x) \; \ mathrm {d} x}$${\ displaystyle f (x)}$${\ displaystyle \ mathrm {d} x}$

## 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.

${\ displaystyle \ int _ {0} ^ {T} f (t) \; \ mathrm {d} t,}$

${\ displaystyle \ int \ limits _ {0} ^ {T} f (t) \; \ mathrm {d} t}$

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.

Coding in Unicode, HTML and LaTeX
character Unicode designation HTML Latex
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 counter-clockwise 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;