Sentence examples for improper integral from inspiring English sources

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The term "improper integral" is correct and usable in written English.
It is a mathematical term used to describe an integral that does not have a finite value, typically because one or both of the limits of integration are infinite or the function being integrated has a singularity within the interval of integration. Example: The function f(x) = 1/x has an improper integral from 1 to ∞, which can be evaluated using the limit as b approaches ∞ of the definite integral from 1 to b.

Dictionary

improper integral

noun

An integral where at least one of the endpoints is taken as a limit, either to a specific number or to infinity.

Exact(35)

Fix, assuming that the improper integral converges.

Boundary Value Problems

(Improper integral) ∫ 0 1 e − 1 x x 2 dx.

Mathematical Sciences

Note that the improper integral on the right is divergent.

Advances in Difference Equations

(i) the improper integral (7.55) . the improper integral (7.55). is finite, whenever is oscillatory and is not oscillatory, (ii) the improper integral (7.56) . the improper integral (7.56). is finite, whenever is not oscillatory and is oscillatory.

Journal of Inequalities and Applications

(i) the improper integral (3.18). is finite, whenever is oscillatory and is not oscillatory; (ii the improper integral (3.19). is finite, whenever is not oscillatory and is oscillatory.

Journal of Inequalities and Applications

provided this limit exists, and one says that the improper integral converges in this case.

Advances in Difference Equations

Similar(25)

In particular, HL integrability encompasses improper integrals of Bochner integrable mappings.

Boundary Value Problems

Moreover HL integrability encloses improper integrals on finite intervals; HK integrability also on unbounded intervals.

Boundary Value Problems

Thus, g is HL integrable because HL integrability encloses improper integrals on finite intervals by Remarks 2.2.

Boundary Value Problems

A few numerical examples are shown to assess the applicaBoththeof the method, its computational effort and some convergence issues.

Engineering Structures

provided that the improper integrals involved are convergent.

Advances in Difference Equations

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