improper integral

American  

[im-prop-er in-ti-gruhl] / ˈɪmˌprɒp ər ˈɪn tɪ grəl /

noun

Mathematics.

1. Also called infinite integral.  a definite integral in which one or both of the limits of integration is infinite.

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

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improper integral British  

noun

1. a definite integral having one or both limits infinite or having an integrand that becomes infinite within the limits of integration

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Etymology

Origin of improper integral

First recorded in 1940–45

Example Sentences

This test, called the integral test, compares an infinite sum to an improper integral.

From Textbooks • Mar. 30, 2016

Use Fubini’s theorem to evaluate the improper integral.

From Textbooks • Mar. 30, 2016

State whether the improper integral converges or diverges.

From Textbooks • Mar. 30, 2016

The convergence or divergence of an improper integral may be determined by comparing it with the value of an improper integral for which the convergence or divergence is known.

From Textbooks • Mar. 30, 2016

Since the improper integral diverges to +∞, the area of the region is infinite.

From Textbooks • Mar. 30, 2016