# At a Glance - 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.

#### Exercise 1

Use the *p*-test to determine if the integral converges or diverges.

#### Exercise 2

Use the *p*-test to determine if the integral converges or diverges.

#### Exercise 3

Use the *p*-test to determine if the integral converges or diverges.

#### Exercise 4

Use the *p*-test to determine if the integral converges or diverges.