Integral symbol

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The integral symbol:

? (Unicode), ${\displaystyle \displaystyle \int }$ (LaTeX)

is used to denote integrals and antiderivatives in mathematics.

Video Integral symbol

History

The notation was introduced by the German mathematician Gottfried Wilhelm Leibniz in 1675 in his private writings; it first appeared publicly in the paper "De Geometria Recondita et analysi indivisibilium atque infinitorum" (On a hidden geometry and analysis of indivisibles and infinites), published in Acta Eruditorum in June 1686. The symbol was based on the s (long s) character, and was chosen because Leibniz thought of the integral as an infinite sum of infinitesimal summands.

Maps Integral symbol

Typography in Unicode and LaTeX

Fundamental symbol

The integral symbol is U+222B ? INTEGRAL in Unicode and \int in LaTeX. In HTML, it is written as ∫ (hexadecimal), ∫ (decimal) and ∫ (named "entity").

The original IBM PC code page 437 character set included a couple of characters ? and ? (codes 244 and 245, respectively) to build the integral symbol. These were deprecated in subsequent MS-DOS code pages, but they still remain in Unicode (U+2320 and U+2321, respectively) for compatibility.

The ? symbol is very similar to, but not to be confused with, the letter ? ("esh").

Extensions of the symbol

Related symbols include:

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Typography in other languages

In other languages, the shape of the integral symbol differs slightly from the shape commonly seen in English-language textbooks. While the English integral symbol leans to the right, the German symbol (used throughout Central Europe) is upright, and the Russian variant leans to the left.

Another difference is in the placement of limits for definite integrals. Generally, in English-language books, limits go to the right of the integral symbol:

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

By contrast, in German and Russian texts, limits for definite integrals are placed above and below the integral symbol, and, as a result, the notation requires larger line spacing:

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

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See also

• Capital sigma notation
• Capital pi notation

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Notes

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References

• Stewart, James (2003). "Integrals". Single Variable Calculus: Early Transcendentals (5th ed.). Belmont, CA: Brooks/Cole. p. 381. ISBN 0-534-39330-6. 
• Zaitcev, V.; Janishewsky, A.; Berdnikov, A. (1999), "Russian Typographical Traditions in Mathematical Literature" (PDF), Russian Typographical Traditions in Mathematical Literature, EuroTeX'99 Proceedings 

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External links

• Fileformat.info

Source of the article : Wikipedia