When does an integral diverge?
Understand the Problem
The question is asking about the conditions under which an integral diverges, which means it seeks to understand the criteria that determine whether the value of an integral can be infinite or not.
Answer
If the limit is ±∞ or does not exist, the integral diverges.
If the limit of the integral exists and is finite, the integral converges. If the limit is ±∞ or does not exist, the integral diverges.
Answer for screen readers
If the limit of the integral exists and is finite, the integral converges. If the limit is ±∞ or does not exist, the integral diverges.
More Information
Understanding convergence and divergence of integrals is essential for evaluating the behavior of integrals that do not have obvious antiderivatives.
Tips
A common mistake is not properly evaluating the limit, especially with respect to infinite limits or discontinuities.
Sources
- Sec_ImproperIntegrals - Convergence and Divergence - sfu.ca
- Determine when an Integral Diverges | Calculus - Study.com - study.com
- Integral Diverges / Converges: Meaning, Examples - Statistics How To - statisticshowto.com
