ABSTRACT

There is an important group of definite integrals, which has not yet been

considered, containing what are called improper integrals. These are definite

integrals in which either the integrand becomes infinite at some point in the

interval of integration, or in which the length of the interval of integration

itself is infinite in length; some integrals are improper in both of these ways.

The question to be answered in such cases is whether the integral has a finite

value. If the value of the integral can be shown to be a finite number I , the

integral is said to be convergent, and to converge to the value I . If the value of the integral is infinite, or undefined, then the integral is said to be divergent.