improper integral


Also found in: Encyclopedia, Wikipedia.

improper integral

n.
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

n
(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


n.
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]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
References in periodicals archive ?
Following this strategy, previously developed in [6], let us consider the random improper integral
Furthermore, the concept of the absolute convergence of a fuzzy improper integral does not make sense in the fuzzy literature.
where the integral is the usual Riemann improper integral and [alpha] [member of] (0,1].
then the Ito integral [bar.Y](0, [omega]) can be used to approximate the improper integral (26), where
The initial IPS might show an obvious gradient in range direction, which is caused by the improper integral constant.
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].
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.
If a [member of] T, sup T = ot and f is rd-continuous on [a, [infinity]), then one defines the improper integral by
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.
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.
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
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.