improper integral

An integral having at least one nonfinite limit or an integrand that becomes infinite between the limits of integration.

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.

improper integral

(Mathematics) a definite integral having one or both limits infinite or having an integrand that becomes infinite within the limits of integration

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

improp′er in′tegral

1. a definite integral whose area of integration is infinite.

2. a definite integral in which the integrand becomes infinite at a point or points in the interval of integration.

[1940–45]

References in periodicals archive ?

Following this strategy, previously developed in [6], let us consider the random improper integral

Analytic-Numerical Solution of Random Parabolic Models: A Mean Square Fourier Transform Approach

Furthermore, the concept of the absolute convergence of a fuzzy improper integral does not make sense in the fuzzy literature.

Aumann Fuzzy Improper Integral and Its Application to Solve Fuzzy Integro-Differential Equations by Laplace Transform Method

where the integral is the usual Riemann improper integral and [alpha] [member of] (0,1].

Generalization of Hermite-Hadamard Type Inequalities via Conformable Fractional Integrals

then the Ito integral [bar.Y](0, [omega]) can be used to approximate the improper integral (26), where

Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations

The initial IPS might show an obvious gradient in range direction, which is caused by the improper integral constant.

Performance Evaluation of Azimuth Offset Method for Mitigating the Ionospheric Effect on SAR Interferometry

Or, if asked to determine whether the improper integral [[integral].sup.[infinity].sub.0] 1/[e.sup.x] + [e.sup.-x] is convergent, we might start by using technology to evaluate [[integral].sup.10.sub.0] 1/[e.sup.x] + [e.sup.-x] dx and [[integral].sup.15.sub.0] 1/[e.sup.x] + [e.sup.-x].

An eclectic approach to the teaching of calculus

it is possible to conclude that the first integral at the second member of (17) is an improper integral of a non-oscillating function which decays asymptotically as [mathematical expression not reproducible], while the last one is a proper integral.

Complex Resonances of a Rectangular Patch in a Multilayered Medium: A New Accurate and Efficient Analytical Technique

If a [member of] T, sup T = ot and f is rd-continuous on [a, [infinity]), then one defines the improper integral by

Periodic solutions for shunting inhibitory cellular neural networks of neutral type with time-varying delays in the leakage term on time scales

for t [greater than or equal to] T and the improper integral of the larger function converges for [absolute value of v] < k, then by the comparison test, the integral [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] converges for [absolute value of v] < k.

A new integral transform

The function [g.sub.1] must guarantee the convergence of the improper integral (27) (i.e., the existence of [u.sub.1]), and the fact that this function [u.sub.1] is solution of the Neumann problems with f = 0.

Green function of the Laplacian for the Neumann problem in [R.sup.n.sub.+]

approaches a finite limit as A [right arrow] [infinity], then we call that limit the improper integral of first kind of f from a to[infinity]and write

Function spaces and their dual spaces on time scales

In contrast with the usual convolution algorithm, the nonhistory-dependent algorithm described in the previous section needs the replacement of the improper integral by a finite sum.