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

State whether the improper integral converges or diverges.

From Textbooks • Mar. 30, 2016

We have seen that the integral test allows us to determine the convergence or divergence of a series by comparing it to a related improper integral.

From Textbooks • Mar. 30, 2016

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

From Textbooks • Mar. 30, 2016

State whether the improper integral converges or diverges.

From Textbooks • Mar. 30, 2016

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

From Textbooks • Mar. 30, 2016