# integral

[in-ti-gruh l, in-teg-ruh l] /ˈɪn tɪ grəl, ɪnˈtɛg rəl/
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.
noun
7.
an integral whole.
8.
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.
Origin of integral
1545-1555
1545-55; < Medieval Latin integrālis. See integer, -al1
Related forms
integrality, noun
Synonyms
2. essential, indispensable, requisite.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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Examples from the Web for integrally
Historical Examples
• For both, reality as well as truth are integrally given in eternity.

Henri Bergson
• Not alone is each one integral, but Lincoln is integrally in each.

Clark S. Beardslee
• It is a characteristic of our minds, that they cannot take an object in, which is submitted to them simply and integrally.

John Henry Cardinal Newman
• Is it the sort of unit which we should use as a result of having memorized it integrally?

Harold E. Palmer
• The man who was accused of being denationalized stands as the most integrally and truly American among his contemporaries.

Gilbert Chinard
• I understand why Rome is the real school for learning, integrally, both ancient and modern history.

Po Baroja Baroja
• Its leverage is felt within us as well as without, for expression and thought are integrally bound together.

George Herbert Palmer
• What we were discussing was the idea of a world growing not integrally but piecemeal by the contributions of its several parts.

William James
British Dictionary definitions for integrally

## integral

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
noun (ˈɪntɪɡrəl)
5.
(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) ʃ
6.
a complete thing; whole
Derived Forms
integrality (ˌɪntɪˈɡrælɪtɪ) noun
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
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Word Origin and History for integrally

## integral

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.

Online Etymology Dictionary, © 2010 Douglas Harper
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integrally in Science
 integral   (ĭn'tĭ-grəl)    Adjective  Involving or expressed as an integer or integers.Noun  See definite integral, indefinite integral.
The American Heritage® Science Dictionary