definite integral


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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.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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, ∫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)
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

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]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.definite integral - the integral of a function over a definite intervaldefinite 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)
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
Translations
određeni integral
定積分
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)
They should be familiar with the term "definite integral" and know how to find the antiderivative of a function.
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.
Construct a novel Lyapunov functional composed of fractional-order integral and definite integral terms:
We consider the definite integral [20, section 3.145, formula 2, pages 270-271]
As the screen suggests, this particular device represents an indefinite integral by leaving blanks where the limits of a definite integral might appear.
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.
It is the definite integral of function h(t) which can be calculated by the following Gauss quadrature formula:
the constant of integration vanishes since the integral considered in (2.12) is a definite integral. On using (2.1), we obtain
Let A'(v) and F'(s) denote a new integral transform and the Laplace transform of the definite integral of f(t).