# integral

## integral

[in-ti-gruhl, in-teg-ruhl]
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 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; < Medieval Latin integrālis. See integer, -al1

integrality, noun
integrally, adverb
unintegral, adjective
unintegrally, adverb

2. essential, indispensable, requisite.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
 integral —adj 1. (often foll by to) being an essential part (of); intrinsic (to) 2. intact; entire 3. formed of constituent parts; united 4. maths a.  of or involving an integral b.  involving or being an integer —n 5. maths ʃ 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) 6. a complete thing; whole integrality —n 'integrally —adv

Collins English Dictionary - Complete & Unabridged 10th Edition
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Etymonline
Word Origin & History

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, © 2010 Douglas Harper
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American Heritage
Science Dictionary
 integral  [%PREMIUM_LINK%]     (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. Published by Houghton Mifflin. All rights reserved.
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Example sentences
These considerations were integral to the design, he says.
Space exploration has bred satellite technology, which has become an integral
part of modern living.
Side comment on the path integral formulation of quantum mechanics.
Children detect falseness a mile away, so believing in what you're doing is an
integral part of leading by example.
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