integral sign IntegralSign 2008-05-18 05:08:49 2009-01-21 09:33:18 Definition integrand integrate % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions \usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \theoremstyle{definition} \newtheorem*{thmplain}{Theorem} The {\em integral sign} $$\int$$ is a stylised version of the {\em 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 {\em summa} (`sum').\, The long shape of $\displaystyle\int$ may be thought to symbolically depict the fact that \PMlinkname{integral}{DefiniteIntegral} 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 a 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 {\em integrated}, is the {\em integrand}.