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integral

[in-ti-gruh l, in-teg-ruh l]
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adjective
  1. of, relating 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. Arithmetic. pertaining to or being an integer; not fractional.
  6. Mathematics. pertaining to or involving integrals.
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noun
  1. an integral whole.
  2. Mathematics.
    1. 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.
    2. a primitive.
    3. any of several analogous quantities.Compare improper integral, line integral, multiple integral, surface integral.
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Origin of integral

From the Medieval Latin word integrālis, dating back to 1545–55. See integer, -al1
Related formsin·te·gral·i·ty, nounin·te·gral·ly, adverbun·in·te·gral, adjectiveun·in·te·gral·ly, adverb

Synonyms

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2. essential, indispensable, requisite.
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

Examples from the Web for integral

Contemporary Examples

Historical Examples

  • The State exists only as an integral portion of the United States.

    'Tis Sixty Years Since

    Charles Francis Adams

  • The 'prison scenes' are an integral part in Boswell's psychology.

    James Boswell

    William Keith Leask

  • There, if always with his ship (but that was an integral part of him) he could always be as solitary as he chose.

    Chance

    Joseph Conrad

  • Each Kedy element was the sole personnel of, and was integral with, his vessel.

    Masters of Space

    Edward Elmer Smith

  • It is integral with the rest; its troubles are Basin troubles.

    The Nation's River

    United States Department of the Interior

British Dictionary definitions for integral

integral

adjective (ˈɪntɪɡrəl, ɪnˈtɛɡrəl)
  1. (often foll by to) being an essential part (of); intrinsic (to)
  2. intact; entire
  3. formed of constituent parts; united
  4. maths
    1. of or involving an integral
    2. involving or being an integer
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noun (ˈɪntɪɡrəl)
  1. 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: ʃ
  2. a complete thing; whole
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Derived Formsintegrality (ˌɪntɪˈɡrælɪtɪ), nounintegrally, adverb
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Word Origin and History for integral

adj.

late 15c., "of or pertaining to a whole," from Middle French intégral (14c.), from Medieval Latin integralis "forming a whole," from Latin integer "whole" (see integer). Related: Integrally. As a noun, 1610s, from the adjective.

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Online Etymology Dictionary, © 2010 Douglas Harper
integral in Science

integral

[ĭn′tĭ-grəl]
Adjective
  1. Involving or expressed as an integer or integers.
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Noun
  1. See definite integral indefinite integral.
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The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.