# integral

[in-ti-gruh l, in-teg-ruh l]

- of, relating to, or belonging as a part of the whole; constituent or component: integral parts.
- necessary to the completeness of the whole: This point is integral to his plan.
- consisting or composed of parts that together constitute a whole.
- entire; complete; whole: the integral works of a writer.
- Arithmetic. pertaining to or being an integer; not fractional.
- Mathematics. pertaining to or involving integrals.

- an integral whole.
- Mathematics.
- 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.
- a primitive.
- any of several analogous quantities.Compare improper integral, line integral, multiple integral, surface integral.

## Origin of integral^{}

## Synonyms

See more synonyms on Thesaurus.com2. 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

#### Sex and drugs and rock ‘n’ roll have always been an integral part of her story.

#### Throwing up is an integral part of the ceremony, and shamans encourage it.

#### This is because espionage has become an integral part of American statecraft.

#### At first this is integral to the fantasy; it's visually stimulating.

#### Not so this time, as Fury had an integral reason for being there, and added muscle, brains and plenty of sharp lines.

### Historical Examples

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

'Tis Sixty Years SinceCharles Francis Adams

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

James BoswellWilliam 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.

ChanceJoseph Conrad

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

Masters of SpaceEdward Elmer Smith

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

The Nation's RiverUnited States Department of the Interior

# integral

- (often foll by to) being an essential part (of); intrinsic (to)
- intact; entire
- formed of constituent parts; united
- maths
- of or involving an integral
- involving or being an integer

- 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
- a complete thing; whole

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.

Online Etymology Dictionary, © 2010 Douglas Harper

# integral

[ĭn′tĭ-grəl]

- Involving or expressed as an integer or integers.

The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.