improper integral
Noun
Meaning
improper integral (plural improper integrals)
(mathematics) An integral where at least one of the endpoints is taken as a limit, either to a specific number or to infinity.
Examples
An improper integral occurs when one or more of these conditions is not satisfied.
Since the integrand is a non-negative real-valued function, there is no difference between having a finite Lebesgue integral and having a finite improper integral (as there is say for the function sin(x)/x when integrated over the entire real line).
If the interval is unbounded, for instance at its upper end, then the improper integral is the limit as that endpoint goes to infinity.