# definite integral

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## definite integral

*n.*

**1.**An integral that is calculated between two specified limits, usually expressed in the form

*∫*The result of performing the integral is a number that represents the area under the curve of

^{b}/_{a}ƒ(x)dx.*ƒ(x)*between the limits and the

*x*-axis if

*f(x)*is greater than or equal to zero between the limits.

**2.**The result of an integration performed on a fixed interval.

## definite integral

*n*

(Mathematics)

*maths***a.**the evaluation of the indefinite integral between two limits, representing the area between the given function and the

*x-*axis between these two values of

*x*

**b.**the expression for that function, ∫

*(*

^{b}af*x*)

*dx*, where

*f*(

*x*) is the given function and

*x = a*and

*x = b*are the limits of integration. Where

*F*(

*x*) = ∫

*f*(

*x*)

*dx*, the indefinite integral, ∫

^{b}a

*f*(

*x*)

*dx = F*(

*b*)

*–F*(

*a*)

## def′inite in′tegral

*n.*

the representation, usu. in symbolic form, of the difference in values of a primitive of a given function evaluated at two designated points. Compare indefinite integral.

[1875–80]

ThesaurusAntonymsRelated WordsSynonyms

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Noun | 1. | definite integral - the integral of a function over a definite intervalintegral - the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x) |

Translations

**određeni integral**

**定積分**

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