# 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 $\mathbb{R}^{2}$ or about a closed surface in $\mathbb{R}^{3}$; 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