We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Indefinite Integrals

Indefinite Integrals

The p-Test



We often use integrals of the functions , for various values of p, to help determine whether other integrals converge or diverge.

You already did the work to show this, so we'll just summarize the results. Assuming p is greater than 0 (because otherwise the exponents do weird things),

  •  converges if p < 1 and diverges otherwise.
  •  converges if p > 1 and diverges otherwise.

This is often called the p-test for improper integrals.

People who Shmooped this also Shmooped...