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integral
7 dictionary results for: Integral
Dictionary.com Unabridged (v 1.1) - Cite This Source - Share This
in·te·gral       [in-ti-gruhl, in-teg-ruhl] Pronunciation Key
–adjective
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.Arithmetic. pertaining to or being an integer; not fractional.
6.Mathematics. pertaining to or involving integrals.
–noun
7.an integral whole.
8.Mathematics.
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. Compare improper integral, line integral, multiple integral, surface integral.
[Origin: 1545–55; < ML integrālis. See integer, -al1]

—Related forms
in·te·gral·i·ty, noun
in·te·gral·ly, adverb

—Synonyms 2. essential, indispensable, requisite.
Dictionary.com Unabridged (v 1.1)
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2006.
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American Heritage Dictionary - Cite This Source - Share This
in·te·gral       (ĭn'tĭ-grəl, ĭn-těg'rəl)  Pronunciation Key 
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
    1. Expressed or expressible as or in terms of integers.
    2. Expressed as or involving integrals.

n.  
  1. A complete unit; a whole.
  2. (ĭn'tĭ-grəl) Mathematics
    1. 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.
    2. A definite integral.
    3. 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 (-grāl'ĭ-tē) n., in'te·gral·ly adv.
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The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2006 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Online Etymology Dictionary - Cite This Source - Share This
integral 
1471, "of or pertaining to a whole," from M.Fr. intégral (14c.), from M.L. integralis "forming a whole," from L. integer "whole" (see integer).

Online Etymology Dictionary, © 2001 Douglas Harper
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WordNet - Cite This Source - Share This
integral

adjective
1. existing as an essential constituent or characteristic; "the Ptolemaic system with its built-in concept of periodicity"; "a constitutional inability to tell the truth" [syn: built-in] 
2. 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" 
3. of or denoted by an integer 

noun
1. the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x) 

WordNet® 3.0, © 2006 by Princeton University.
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The American Heritage Science Dictionary - Cite This Source - Share This
integral       (ĭn'tĭ-grəl)  Pronunciation Key 
Adjective  
Involving or expressed as an integer or integers.

Noun  
See definite integral, indefinite integral.

The American Heritage® Science Dictionary
Copyright © 2002 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Webster's Revised Unabridged Dictionary - Cite This Source - Share This

Integral

In"te*gral\, a. [Cf. F. int['e]gral. See Integer.]

1. Lacking nothing of completeness; complete; perfect; uninjured; whole; entire.

A local motion keepeth bodies integral. --Bacon.

2. Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.

Ceasing to do evil, and doing good, are the two great integral parts that complete this duty. --South.

3. (Math.) (a) Of, pertaining to, or being, a whole number or undivided quantity; not fractional. (b) Pertaining to, or proceeding by, integration; as, the integral calculus.

Integral calculus. See under Calculus.

Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
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Webster's Revised Unabridged Dictionary - Cite This Source - Share This

Integral

In"te*gral\, n. 1. A whole; an entire thing; a whole number; an individual.

2. (Math.) An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.

Elliptic integral, one of an important class of integrals, occurring in the higher mathematics; -- so called because one of the integrals expresses the length of an arc of an ellipse.

Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
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