The integral is .

Definition of an improper integral :

If exists for every number , then provoded this limit exists (as a finite number).

Consider .

 is continuous on the interval  and it is not continuous at , then .

Here we need to use a right hand limit, since the interval of integration is entirely on the right side of the lower limit.

Therefore, .

Since (finite value), the integral is convergent.

The integral is convergent and the value is .