IMPROPER INTEGRALS

In defining the Riemann integral

the interval [a,b] of integration is finite and f (x) is finite at every point in [a,b] . In many physical applications, the following types of integrals arise:

Where a is a real number and f(x) is a continuous function on the interval of integration. They are defined as limits of Riemann integral

These are called improper integral of first kind. If the limit exists, then the improper integrals are said to be convergent.

By fundamental theorem of integral calculus, there exists a function F(t) such that