# integral

[ in-ti-gruhl, in-teg-ruhl ]
See synonyms for: integralintegralsintegrality on Thesaurus.com

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.

1. consisting or composed of parts that together constitute a whole.

2. entire; complete; whole: the integral works of a writer.

3. Arithmetic. pertaining to or being an integer; not fractional.

4. Mathematics. pertaining to or involving integrals.

noun
1. an integral whole.

2. 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

1
From the Medieval Latin word integrālis, dating back to 1545–55. See integer, -al1

## Other words from integral

• in·te·gral·i·ty, noun

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2024

## How to use integral in a sentence

• It will be seen that the sixteen cams are forged integrally with the shaft and that it is spur-gear driven.

Aviation Engines | Victor Wilfred Pag
• The man who was accused of being denationalized stands as the most integrally and truly American among his contemporaries.

Thomas Jefferson | Gilbert Chinard
• The northerly cross wall was tied into the brickwork of the east wall, showing that it was built integrally with the foundation.

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

The Teacher | George Herbert Palmer
• In this case, the numeral "1" has been applied with wire fasteners rather than cast integrally with the two portions of the plate.

American Military Insignia 1800-1851 | J. Duncan Campbell and Edgar M. Howell.

## British Dictionary definitions for integral

integral

1. (often foll by to) being an essential part (of); intrinsic (to)

2. intact; entire

1. formed of constituent parts; united

2. maths

• of or involving an integral

• involving or being an integer

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

## Derived forms of integral

• integrality (ˌɪntɪˈɡrælɪtɪ), noun

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

integral

[ ĭntĭ-grəl ]