Integral symbol


The integral symbol:
is used to denote integrals and antiderivatives in mathematics.

History

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

Typography in Unicode and LaTeX

Fundamental symbol

The integral symbol is in Unicode and \int in LaTeX. In HTML, it is written as ∫, ∫ and ∫.
The original IBM PC code page 437 character set included a couple of characters ⌠ and ⌡ to build the integral symbol. These were deprecated in subsequent MS-DOS code pages, but they still remain in Unicode for compatibility.
The ∫ symbol is very similar to, but not to be confused with, the letter ʃ.

Extensions of the symbol

Related symbols include:

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 is upright, and the Russian variant leans slight to the left to occupy less horizontal space.
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:
By contrast, in German and Russian texts, the limits are placed above and below the integral symbol, and, as a result, the notation requires larger line spacing, but is more compact horizontally, especially when longer expressions are used in the limits: