n. a definite integral with one or both limits of integration infinite, or having an integrand that becomes infinite between the limits of integration. The improper integral is said to converge if exists, and to diverge otherwise. Similarly, if the integrand has a singularity at an endpoint of the interval of integration, then the integral is defined as the limit of the proper integrals as the limit of integration tends to that endpoint from within the interval; if the singularity is in the interior of the interval, then the integral is the sum of the two improper integrals on the subintervals above and below the singularity.