# integral

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Related to Integrals: Definite Integrals

## in·te·gral

(ĭn′tĭ-grəl, ĭn-tĕg′rəl)*adj.*

**1.**Essential or necessary for completeness; constituent: The kitchen is an integral part of a house.

**2.**Possessing everything essential; entire.

**3.**(ĭn′tĭ-grəl)

*Mathematics*

**a.**Expressed or expressible as or in terms of integers.

**b.**Expressed as or involving integrals.

*n.*

**1.**A complete unit; a whole.

**2.**(ĭn′tĭ-grəl)

*Mathematics*

**a.**A number computed by a limiting process in which the domain of a function, often an interval or planar region, is divided into arbitrarily small units, the value of the function at a point in each unit is multiplied by the linear or areal measurement of that unit, and all such products are summed.

**b.**A definite integral.

**c.**An indefinite integral.

[Middle English, from Old French, from Medieval Latin integrālis,

*making up a whole*, from Latin integer,*complete*; see**integer**.]**in′te·gral′i·ty**(-grăl′ĭ-tē)

*n.*

**in′te·gral·ly**

*adv.*

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## integral

*adj*

**1.**(

*often foll by to*) being an essential part (of); intrinsic (to)

**2.**intact; entire

**3.**formed of constituent parts; united

**4.**(Mathematics)

*maths*

**a.**of or involving an integral

**b.**involving or being an integer

*n*

**5.**(Mathematics)

*maths*the limit of an increasingly large number of increasingly smaller quantities, related to the function that is being integrated (the integrand). The independent variables may be confined within certain limits (

**definite integral**) or in the absence of limits (

**indefinite integral**). Symbol:

**∫**

**6.**a complete thing; whole

**integrality**

*n*

**ˈintegrally**

*adv*

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## in•te•gral

(ˈɪn tɪ grəl, ɪnˈtɛg rəl)*adj.*

**1.**of or belonging as an essential part of the whole; necessary to completeness; constituent:

*an integral part.*

**2.**composed of parts that together constitute a whole.

**3.**entire; complete; whole.

**4.**pertaining to or being an integer; not fractional.

**5.**pertaining to or involving mathematical integrals.

*n.*

**6.**an integral whole.

**7.**

*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.

**b.**a primitive.

**c.**any of several analogous quantities.

**in`te•gral′i•ty,**

*n.*

**in′te•gral•ly,**

*adv.*

Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.

## in·te·gral

(ĭn′tĭ-grəl)**1.**Involving or expressed as an integer or integers.

**2.**In calculus, the result of integration.

The American Heritage® Student Science Dictionary, Second Edition. Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

ThesaurusAntonymsRelated WordsSynonyms

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Noun | 1. | integral - the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)indefinite integral - the set of functions F(x) + C, where C is any real number, such that F(x) is the integral of f(x) definite integral - the integral of a function over a definite interval |

Adj. | 1. | integral - existing as an essential constituent or characteristic; "the Ptolemaic system with its built-in concept of periodicity"; "a constitutional inability to tell the truth"intrinsic, intrinsical - belonging to a thing by its very nature; "form was treated as something intrinsic, as the very essence of the thing"- John Dewey |

2. | integral - constituting the undiminished entirety; lacking nothing essential especially not damaged; "a local motion keepeth bodies integral"- Bacon; "was able to keep the collection entire during his lifetime"; "fought to keep the union intact"whole - including all components without exception; being one unit or constituting the full amount or extent or duration; complete; "gave his whole attention"; "a whole wardrobe for the tropics"; "the whole hog"; "a whole week"; "the baby cried the whole trip home"; "a whole loaf of bread" | |

3. | integral - of or denoted by an integer |

Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.

## integral

*adjective*

**1.**essential, basic, fundamental, necessary, component, constituent, indispensable, intrinsic, requisite, elemental Rituals form an integral part of any human society.

**unnecessary, unimportant, inessential**

*essential*Collins Thesaurus of the English Language – Complete and Unabridged 2nd Edition. 2002 © HarperCollins Publishers 1995, 2002

## integral

*adjective*

**1.**Constituting or forming part of the essence of something:

*noun*

The American Heritage® Roget's Thesaurus. Copyright © 2013, 2014 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Translations

**integrál**

**integraali**

**integral**

**integrál**

**heildun**

**tegrun**

**integral**

## integral

[ˈɪntɪgr*ə*l]

**A.**

*ADJ*(=

*essential*) [

*part*] → integrante, esencial

it is an integral part of the plan → es parte integrante

*or*esencial del proyecto

Collins Spanish Dictionary - Complete and Unabridged 8th Edition 2005 © William Collins Sons & Co. Ltd. 1971, 1988 © HarperCollins Publishers 1992, 1993, 1996, 1997, 2000, 2003, 2005

## integral

[ɪnˈtɛgrəl ˈɪnt*ɪ*grəl]

*adj*

an integral part of sth → une partie intégrante de qch

to be an integral part of sth, to form an integral part of sth → faire partie intégrante de qch

an integral element of sth → un élément constitutif de qch, un élément à part entière de qch

an integral component of sth → un composant à part entière de qch

to play an integral role in sth → jouer un rôle à part entière dans qch

to be integral to sth → faire partie intégrante de qchintegral calculus

*n*→ calcul

*m*intégral

Collins English/French Electronic Resource. © HarperCollins Publishers 2005

## integral

*adj*

*part*→ wesentlich, integral

*(geh)*; to be

**integral**to something → ein wesentlicher Bestandteil einer Sache

*(gen)*→ sein; to play an

**integral**role in something → eine wesentliche Rolle bei etw spielen

(= whole) → vollständig, vollkommen

(Math) → Integral-

Collins German Dictionary – Complete and Unabridged 7th Edition 2005. © William Collins Sons & Co. Ltd. 1980 © HarperCollins Publishers 1991, 1997, 1999, 2004, 2005, 2007

## integral

[ˈɪntɪgr__/ə__l]

Collins Italian Dictionary 1st Edition © HarperCollins Publishers 1995

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