Notation
Isaac Newton Sir Isaac Newton, FRS , was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is considered one of the most influential people in human history. His Philosophiæ Naturalis Principia Mathematica, published in 1687, is by itself considered to be among the most influential books in the history of used a small vertical bar above a variable to indicate integration, or placed the variable inside a box. The vertical bar was easily confused with or , which Newton used to indicate differentiation, and the box notation was difficult for printers to reproduce, so these notations were not widely adopted.
The modern notation for the indefinite integral was introduced by Gottfried Leibniz Gottfried Wilhelm Leibniz was a German philosopher and mathematician who wrote primarily in Latin and French in 1675 (Burton 1988, p. 359; Leibniz 1899, p. 154). He adapted the integral symbol The ∫ symbol is used to denote the integral in mathematics. The notation was introduced by the German mathematician Gottfried Wilhelm von Leibniz towards the end of the 17th century. The symbol was based on the ſ character, and was chosen because the integral is a limit of sums. See long s for more details on the history of ſ, ∫, from an elongated letter s The long, medial or descending s is a form of the minuscule letter 's' formerly used where 's' occurred in the middle or at the beginning of a word, for example ſinfulneſs ("sinfulness"). The modern letterform was called the terminal or short s, standing for summa (Latin for "sum" or "total"). The modern notation for the definite integral, with limits above and below the integral sign, was first used by Joseph Fourier Jean Baptiste Joseph Fourier was a French mathematician and physicist best known for initiating the investigation of Fourier series and their application to problems of heat transfer. The Fourier transform and Fourier's Law are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect in Mémoires of the French Academy around 1819–20, reprinted in his book of 1822 (Cajori 1929, pp. 249–250; Fourier 1822, §231).
<<Table of Contents Integration is an important concept in mathematics which, together with differentiation, forms one of the main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integral | Next>> | Show All>>
