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.