integral sign

The integral sign

is a stylised version of the long s letter.

The long s is a typographic variant of lowercase s, being the only lowercase s in the Carolingian minuscule script.  The modern short (round) s appeared later to the ends of words, and has now replaced completely the long s in the antiqua script.

Gottfried Wilhelm Leibniz introduced the integral sign as the first letter s of the Latin word summa (‘sum’).  The long shape of may be thought to symbolically depict the fact that is a limiting case of sum.

A variant

of the integral sign is used in integrals taken along a closed curve in 2 or about a closed surface in 3; see e.g. Cauchy integral theorem, derivation of heat equation.

The function given after the integral sign, i.e. the function to be integrated, is the integrand.

Title integral sign
Canonical name IntegralSign
Date of creation 2013-03-22 18:04:00
Last modified on 2013-03-22 18:04:00
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 7
Author pahio (2872)
Entry type Definition
Classification msc 00A05
Classification msc 00A06
Related topic RiemannIntegral
Related topic RiemannStieltjesIntegral
Related topic Integral2
Defines integrand
Defines integrate