definite integral

n.1. An integral that is calculated between two specified limits, usually expressed in the form ∫ ^b/_a ƒ(x)dx. The result of performing the integral is a number that represents the area under the curve of 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 xb. the expression for that function, ∫^baf(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, ∫^baf(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]

Thesaurus

Noun

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

Definite Integral

one of the fundamental concepts of mathematical analysis; the solution of a number of problems in geometry, mechanics, and physics reduces to a definite integral. The definite integral is a number equal to the limit of the sums of a particular type (integral sums) corresponding to a function f(x) and an interval [a, b]; it is denoted by . Geometrically, the definite integral expresses the area of a “curvilinear trapezoid” bounded by the interval [a, b] on the x-axis, the graph of the function f(x), and the ordinates of the points on the graph that have abscissas a and b. For a precise definition and generalization of the definite integral, seeINTEGRAL and INTEGRAL CALCULUS.

definite integral