# 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 $\int$ 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 |