definite integral

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.

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definite integral

(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, ∫^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)

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def′inite in′tegral

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 WordsSynonymsLegend:

Noun

definite integral - the integral of a function over a definite interval

integral - 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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References in periodicals archive

Among the topics are prerequisites for calculus, the derivative and its applications, techniques for integration and improper integrals, and applications of the definite integral. ([umlaut] Ringgold, Inc., Portland, OR)

Single Variable Calculus: A First Step

They should be familiar with the term "definite integral" and know how to find the antiderivative of a function.

STEM integration: solids, CAD, and 3D printers: Some topics in mathematics more intuitively lend themselves to ignite a deeper interest in STEM applications

The BP neural network algorithm was used in this study to fit the F-s curve, and then the definite integral method was used to achieve the shear energy dissipation of lime-reinforced iron tailings powder.

Shearing Performance of Lime-Reinforced Iron Tailing Powder Based on Energy Dissipation

Construct a novel Lyapunov functional composed of fractional-order integral and definite integral terms:

Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

We consider the definite integral [20, section 3.145, formula 2, pages 270-271]

Closed-Form Exact Solutions for the Unforced Quintic Nonlinear Oscillator

where we have defined the definite integral operator [L.sup.-1.sub.1] as

Exact and Approximate Analytic Solutions of the Jeffery-Hamel Flow Problem by the Duan-Rach Modified Adomian Decomposition Method

As the screen suggests, this particular device represents an indefinite integral by leaving blanks where the limits of a definite integral might appear.

Integrating technologies into mathematics: comparing the cases of square roots and integrals

Then the field is open to deal with anti-derivatives and solve simple differential equations, well before the definite integral is introduced through sequences of Riemann sums.

An eclectic approach to the teaching of calculus

It is the definite integral of function h(t) which can be calculated by the following Gauss quadrature formula:

Application of radial basis function method for solving nonlinear integral equations

the constant of integration vanishes since the integral considered in (2.12) is a definite integral. On using (2.1), we obtain

Relations for marginal and joint moment generating functions of extended type I generalized logistic distribution based on lower generalized order statistics and characterization

Let A'(v) and F'(s) denote a new integral transform and the Laplace transform of the definite integral of f(t).

A new integral transform