integral


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 plan.
3. consisting or composed of parts that together constitute a whole.
4. entire; complete; whole: the integral works of a writer.
5. Arith. pertaining to or being an integer; not fractional.
6. Math. pertaining to or involving integrals.
n.
7. an integral whole.
8. Math.
a. Also called Riemann integral. the numerical measure of the area bounded above by the graph of a given function, below by the x-axis, and on the sides by ordinates drawn at the endpoints of a specified interval; the limit, as the norm of partitions of the given interval approaches zero, of the sum of the products of the function evaluated at a point in each subinterval times the length of the subinterval.
b. a primitive.
c. any of several analogous quantities. Cf. improper integral, line integral, multiple integral, surface integral.
[1545-55; < ML integralis. See INTEGER, -AL1]
Syn. 2. essential, indispensable, requisite.

* * *

I
Fundamental concept of calculus related to areas and other quantities modeled by functions.

A definite integral gives the area between the graph of a function and the horizontal axis between vertical lines at the endpoints of an interval. It also calculates the net change in a system over an interval, thus leading to formulas for the work done by a varying force or the distance traveled by an object moving at varying speeds. When only the function is given, with no interval, it is known as an indefinite integral. The process of solving either a definite or an indefinite integral is called integration. According to the fundamental theorem of calculus, a definite integral can be calculated by using its antiderivative (a function whose rate of change, or derivative, equals the function being integrated). Integrals extend to higher dimensions through multiple integrals. See also line integral; surface integral.
II
(as used in expressions)

* * *

      in mathematics, either a numerical value equal to the area under the graph of a function for some interval (definite integral) or a new function the derivative of which is the original function (indefinite integral). These two meanings are related by the fact that a definite integral of any function that can be integrated can be found using the indefinite integral and a corollary to the fundamental theorem of calculus. The definite integral (also called Riemann integral) of a function f(x) is denoted as

      (see integration [for symbol]) and is equal to the area of the region bounded by the curve (if the function is positive between x = a and x = b) y = f(x), the x-axis, and the lines x = a and x = b. An indefinite integral, sometimes called an antiderivative, of a function f(x), denoted by

      is a function the derivative of which is f(x). Because the derivative of a constant is zero, the indefinite integral is not unique. The process of finding an indefinite integral is called integration.

* * *


Universalium. 2010.

Synonyms:

Look at other dictionaries:

  • intégral — intégral, ale, aux [ ɛ̃tegral, o ] adj. et n. f. • 1640 ; parties intégralesXIVe; lat. integralis, de integer « entier » I ♦ Cour. Qui n est l objet d aucune diminution, d aucune restriction. ⇒ 1. complet, entier. Remboursement intégral.… …   Encyclopédie Universelle

  • integral — INTEGRÁL, Ă, integrali, e, adj., s.f. 1. adj. (Adesea adverbial) Întreg, complet. ♢ Făină integrală = făină brută obţinută prin măcinarea grâului. Pâine integrală = pâine fabricată din făină integrală. 2. adj. (În sintagmele) Calcul integral =… …   Dicționar Român

  • Integral — «Integral»  песня английской поп группы Pet Shop Boys. Это четвёртый сингл с альбома «Fundamental». Вышел в свет 8 октября 2007. Сингл доступен только для скачивания, а два ремикса на «Integral» были промо версией к сборнику ремиксов «Disco… …   Википедия

  • intégral — intégral, ale (in té gral, gra l ) adj. 1°   Entier, qui n éprouve aucune diminution. Des payements intégraux. Restitution intégrale. Le renouvellement intégral d une chambre législative. 2°   Terme de mathématique. Calcul inverse du calcul… …   Dictionnaire de la Langue Française d'Émile Littré

  • integral — adjetivo 1. Que contiene todos los aspectos o todas las partes de un todo: educación integral. Pretendemos una reforma integral. 2. Área: matemáticas [Signo] que indica la integración. sustantivo femenino …   Diccionario Salamanca de la Lengua Española

  • Integral — In te*gral, a. [Cf. F. int[ e]gral. See {Integer}.] [1913 Webster] 1. Lacking nothing of completeness; complete; perfect; uninjured; whole; entire. [1913 Webster] A local motion keepeth bodies integral. Bacon. [1913 Webster] 2. Essential to… …   The Collaborative International Dictionary of English

  • Integral — ist: in der Analysis ein Grenzwert, zum Beispiel zur Berechnung von Flächen und Volumina, siehe Integralrechnung in der Maßtheorie der erweiterte Integralbegriff, siehe Lebesgue Integral in Mathematik und Physik allgemein die Lösung einer… …   Deutsch Wikipedia

  • integral — (Del b. lat. integrālis). 1. adj. Global, total. 2. Fil. Dicho de cada una de las partes de un todo: Que entra en su composición sin serle esencial, de manera que el todo puede subsistir, aunque incompleto, sin ella. 3. Mat. Se dice del signo (∫) …   Diccionario de la lengua española

  • INTEGRAL — Intégral Cette page d’homonymie répertorie les différents sujets et articles partageant un même nom. INTEGRAL est un sigle pouvant faire référence à : International Gamma Ray Astrophysics Laboratory, un satellite artificiel, Integral peut… …   Wikipédia en Français

  • Integral — Intégral Cette page d’homonymie répertorie les différents sujets et articles partageant un même nom. INTEGRAL est un sigle pouvant faire référence à : International Gamma Ray Astrophysics Laboratory, un satellite artificiel, Integral peut… …   Wikipédia en Français

  • integral — UK US /ˈɪntɪgrəl/ adjective ► necessary and important as a part of something: »He s an integral part of the team and we can t do without him. integral to sth »The reliability of our suppliers has been integral to the company s success …   Financial and business terms


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.