integral sign

The integral sign

$$\int$$

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 ${\displaystyle \int }$ may be thought to symbolically depict the fact that http://planetmath.org/DefiniteIntegralintegral is a limiting case of sum.

A variant

$$\oint$$

of the integral sign is used in integrals taken along a closed curve in ${ℝ}^2$ or about a closed surface in ${ℝ}^3$; 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