in·​te·​gral | \ ˈin-ti-grəl (usually so in mathematics) How to pronounce integral (audio) ; in-ˈte-grəl How to pronounce integral (audio) also -ˈtē- also nonstandard ˈin-trə-gəl \

Definition of integral

 (Entry 1 of 2)

1a : essential to completeness : constituent an integral part of the curriculum
b(1) : being, containing, or relating to one or more mathematical integers
(2) : relating to or concerned with mathematical integration or the results of mathematical integration
c : formed as a unit with another part a seat with integral headrest
2 : composed of constituent parts
3 : lacking nothing essential : entire


in·​te·​gral | \ ˈin-ti-grəl (usually so in mathematics) How to pronounce integral (audio) ; in-ˈte-grəl also -ˈtē- also nonstandard ˈin-trə-gəl \

Definition of integral (Entry 2 of 2)

: the result of a mathematical integration — compare definite integral, indefinite integral

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Other Words from integral


integrality \ ˌin-​tə-​ˈgra-​lə-​tē How to pronounce integral (audio) \ noun
integrally \ ˈin-​ti-​grə-​lē How to pronounce integral (audio) ; in-​ˈte-​grə-​ also  -​ˈtē-​ \ adverb

Examples of integral in a Sentence

Adjective I do know that shoot-'em-ups (and saw-'em-ups) are likely to remain part of our lives, and that suggests a depressing idea: Maybe the love of violence is an integral part of human nature … — Stephen King, Entertainment Weekly, 12 Oct. 2007 Stuffed with peanut butter, celery is the quintessential after-school snack; diced, it provides an essential crunch to chicken and potato salads; buttered up, it is an integral part of Thanksgiving stuffing. — Sara Dickerman, New York Times Magazine, 3 Sept. 2006 Sitting out on the grass … watching the freight trains roll by on the levee at two in the morning, drinking a beer and listening to the music drifting out of the club, is an integral part of the whole experience. — Tom Piazza, Why New Orleans Matters, 2005 She had become an integral part of their lives. a car dealer respected for his integral honesty and straightforwardness with customers Noun The main tools used in the study of these functions are those we have already discussed: representation as integrals, power-series expansions, and differential equations. — Robert S. Strichartz, The Way of Analysis, 2000
Recent Examples on the Web: Adjective Text messaging was an integral part of the food delivery process, especially for those who live in remote locations without clear directions. Delaney White, The Arizona Republic, "Long hours, remote locations: How a Navajo Marine helped families living far from access," 1 May 2021 Nicki James, class president of Westminster’s class of 2022, said prom is an integral part of the high school experience and the cancellation was a huge disappointment. Kristen Griffith,, "With school-sponsored proms canceled, students and parents make alternative plans," 30 Apr. 2021 Community gardens have been an integral part of Portland neighborhoods since they were first established in 1975. oregonlive, "See how Portland’s community gardens are growing this spring," 29 Apr. 2021 Boynton Beach resident Barry Davis, who was born in the Bronx, has been an integral part of the league as treasurer and secretary while also previously handling the commissioner role. Alex Kushel,, "Palm Beach County Stickball League’s upcoming season set for October," 29 Apr. 2021 Driven by clamoring sustainability mindsets and regulatory mandates, companies are increasingly making the circular economy an integral part of their business model. Elif Kuralay, Forbes, "Three Practical Steps To Gain Business Value In The Second-Hand Economy," 28 Apr. 2021 Hiring a diverse staff will also be an integral part of the couple’s inclusion efforts, McDaniel said. NBC News, "Bucking a national trend, a new queer bar is set to open in D.C.," 28 Apr. 2021 The companies that thrive in it will be the ones that recognize this now, and make security an integral part of their plans from the beginning, not something that is considered after the plans have already been made. Jesper Andersen, Fortune, "The hybrid office will create great opportunities—for companies and cybercriminals," 27 Apr. 2021 An enduring expression of this bond with the movies and their stars is an integral part of what is often considered a superficial annual tradition—the Academy Awards. Peter Tonguette, WSJ, "Why People Care So Much About ‘In Memoriam’ at the Oscars," 24 Apr. 2021 Recent Examples on the Web: Noun To tally the possibilities implied by a loop, theorists must turn to a summing operation known as an integral. Quanta Magazine, "The Mathematical Structure of Particle Collisions Comes Into View," 20 Aug. 2020 But there is one small mercy: Physicists don’t need to calculate every last integral in a complicated Feynman diagram because the vast majority can be lumped together. Quanta Magazine, "The Mathematical Structure of Particle Collisions Comes Into View," 20 Aug. 2020 Progress, and much needed for a starter integral to Oakland’s hopes of winning the division and going deep into the postseason. Susan Slusser,, "Sean Manaea shows good signs and A’s, powered by Mark Canha, get another late win," 15 Aug. 2020 Physicists then take the integral of every possible path an experiment could follow from beginning to end and add those integrals together. Quanta Magazine, "The Math That’s Too Difficult for Physics," 18 Nov. 2016

These example sentences are selected automatically from various online news sources to reflect current usage of the word 'integral.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

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First Known Use of integral


1551, in the meaning defined at sense 1a


circa 1741, in the meaning defined above

History and Etymology for integral


see integer


see integer

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Time Traveler for integral

Time Traveler

The first known use of integral was in 1551

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Statistics for integral

Last Updated

4 May 2021

Cite this Entry

“Integral.” Dictionary, Merriam-Webster, Accessed 11 May. 2021.

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More Definitions for integral



English Language Learners Definition of integral

: very important and necessary


in·​te·​gral | \ ˈin-ti-grəl How to pronounce integral (audio) \

Kids Definition of integral

: very important and necessary : needed to make something complete an integral part

Comments on integral

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