definite integral

definite integral
Integration In`te*gra"tion ([i^]n`t[-e]*gr[=a]"sh[u^]n), n. [L. integratio a renewing, restoring: cf. F. int['e]gration.] [1913 Webster] 1. The act or process of making whole or entire. [1913 Webster]

2. (Math.) The operation of finding the primitive function which has a given function for its differential coefficient. See {Integral}. [1913 Webster]

Note: The symbol of integration is [integral2l] (standing for the Latin summa sum), and the integral is also regarded as the limiting value of the sum of great numbers of differentials, when the magnitude of the differentials decreases, and their number increases indefinitely. See {Limit}, n. When the summation is made between specified values of the variable, the result is a {definite integral}, and those values of the variable are the limits of the integral. When the summation is made successively for two or more variables, the result is a {multiple integral}. [1913 Webster]

3. In the theory of evolution: The process by which the manifold is compacted into the relatively simple and permanent. It is supposed to alternate with differentiation as an agent in development. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

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  • definite integral — n. Math. an integral in which the range of integration is specified: its value equals the area on a graph bounded by a curve, the x axis, and two given ordinates …   English World dictionary

  • definite integral — noun the integral of a function over a definite interval • Hypernyms: ↑integral …   Useful english dictionary

  • definite integral — noun The integral of a function between an upper and lower limit See Also: indefinite integral …   Wiktionary

  • definite integral — noun Date: 1834 the difference between the values of the integral of a given function f(x) for an upper value b and a lower value a of the independent variable x …   New Collegiate Dictionary

  • definite integral — Math. the representation, usually in symbolic form, of the difference in values of a primitive of a given function evaluated at two designated points. Cf. indefinite integral. [1875 80] * * * …   Universalium

  • definite integral — noun Mathematics an integral expressed as the difference between values at specified upper and lower limits of the independent variable …   English new terms dictionary

  • definite integral — def′inite in′tegral n. math. the representation, usu. in symbolic form, of the difference in values of a primitive of a given function evaluated at two designated points Compare indefinite integral • Etymology: 1875–80 …   From formal English to slang

  • integral — [in′tə grəl; ] often, for adj. 1 3 [, in teg′rəl] adj. [LL integralis < L integer: see INTEGER] 1. necessary for completeness; essential [an integral part] 2. whole or complete 3. made up of parts forming a whole 4. Math …   English World dictionary

  • Integral — This article is about the concept of integrals in calculus. For the set of numbers, see integer. For other uses, see Integral (disambiguation). A definite integral of a function can be represented as the signed area of the region bounded by its… …   Wikipedia

  • integral — integrality, n. integrally, adv. /in ti greuhl, in teg reuhl/, adj. 1. of, pertaining to, or belonging as a part of the whole; constituent or component: integral parts. 2. necessary to the completeness of the whole: This point is integral to his… …   Universalium

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