# integral

^{1}in·te·gral

*adjective*\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*

## Examples of *INTEGRAL*

- She had become an
*integral*part of their lives. - <a car dealer respected for his
*integral*honesty and straightforwardness with customers> - 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 - [+]more

## Origin of *INTEGRAL*

## 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

^{2}in·te·gral

*noun*\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

## Origin of *INTEGRAL*

## Other Mathematics and Statistics Terms

## integral

*noun*

*(Concise Encyclopedia)*

Fundamental concept of calculus related to areas and other quantities modeled by functions. A definite integral gives the area between the graph of a function and the horizontal axis between vertical lines at the endpoints of an interval. It also calculates the net change in a system over an interval, thus leading to formulas for the work done by a varying force or the distance traveled by an object moving at varying speeds. When only the function is given, with no interval, it is known as an indefinite integral. The process of solving either a definite or an indefinite integral is called integration. According to the fundamental theorem of calculus, a definite integral can be calculated by using its antiderivative (a function whose rate of change, or derivative, equals the function being integrated). Integrals extend to higher dimensions through multiple integrals. *See also* line integral; surface integral.

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