En cálculo, una integral impropia es el límite de una integral definida cuando uno o ambos extremos del intervalo de integración se acercan a un número real específico, a ∞, o a −∞. Además una integral definida es impropia cuando la función integrando de la integral definida no es continua en todo el intervalo de integración. También se pueden dar ambas situaciones.

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In mathematical analysis, an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number or or or, in some cases, as both endpoints approach limits. Such an integral is often written symbolically just like a standard definite integral, in some cases with infinity as a limit of integration. Specifically, an improper integral is a limit of the form or of the form in which one takes a limit in one or the other (or sometimes both) endpoints (, §10.23). By abuse of notation, improper integrals are often written symbolically just like standard definite integrals, perhaps with infinity among the limits of integration. When the definite integral exists (in the sense of either the Riemann integral or the more advanced Lebesgue integral), this ambiguity is resolved as both the proper and improper integral will coincide in value. Often one is able to compute values for improper integrals, even when the function is not integrable in the conventional sense (as a Riemann integral, for instance) because of a singularity in the function or because one of the bounds of integration is infinite.

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