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

  1. She had become an integral part of their lives.
  2. <a car dealer respected for his integral honesty and straightforwardness with customers>
  3. 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

Origin of INTEGRAL

(see integer)
First Known Use: 1551


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

  1. 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

(see integer)
First Known Use: circa 1741

Other Mathematics and Statistics Terms

abscissa, denominator, divisor, equilateral, exponent, hypotenuse, logarithm, oblique, radii, rhomb


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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