An improper integral — one with an infinite bound or an integrand that is unbounded (or undefined) somewhere on the interval of integration — is evaluated as a limit of a proper (definite) integral as the problematic bound approaches infinity or approaches the point of discontinuity; the improper integral converges if this limit exists and is finite, and diverges otherwise. This belongs to the theory of improper integrals in single-variable calculus, an extension of the definite integral (Fundamental Theorem of Calculus) to unbounded domains or unbounded integrands, and relies on limit evaluation techniques including L'Hopital's rule and the additive splitting of integrals at points of discontinuity.
An improper integral — one with an infinite bound or an integrand that is unbounded (or undefined) somewhere on the interval of integration — is evaluated as a limit of a proper (definite) integral a…