improper integral

A definite integral that covers an unbounded area

1. Unbounded endpoint: At least one endpoint is , for example

2. Unbounded function: Finite endpoints, but the integrated function in unbounded at at least one of them, for example:

Process

Evaluation Process

1. Consider the integral as the limit, see the definition above
2. Integrate the function to get the definite integral
3. Find the limit of the result from step 2.
4. Conclude whether the integral converges (=its limit exists) or diverges

Examples

(Example)

Example