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# 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.

#### Example 1

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

#### 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.

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