¹integral

adjective in·te·gral \ˈin-ti-grəl (usually so in mathematics); in-ˈte-grəl also -ˈtē- also ÷ˈin-trə-gəl\

: very important and necessary

Full Definition of INTEGRAL

a : 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>

: composed of constituent parts

: lacking nothing essential : entire

— in·te·gral·i·ty \ˌin-tə-ˈgra-lə-tē\ noun

— in·te·gral·ly \ˈin-ti-grə-lē; in-ˈte-grə- also -ˈtē-\ adverb

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Examples of INTEGRAL

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
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Origin of INTEGRAL

(see integer)

First Known Use: 1551

Related to INTEGRAL

Synonyms: built-in, constitutional, constitutive, essential, hardwired, immanent, inborn, inbred, indigenous, ingrain, ingrained (also engrained), innate, inherent, intrinsic, native, natural

Antonyms: adventitious, extraneous, extrinsic

²integral

noun in·te·gral \ˈin-ti-grəl (usually so in mathematics); in-ˈte-grəl also -ˈtē- also ÷ˈin-trə-gəl\

Definition of INTEGRAL

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

Examples of INTEGRAL

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