From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!

# At a Glance - Comparison with Formulas

We can figure out whether integrals converge or diverge by comparing them with other integrals whose convergence or divergence we already know. When we're looking at formulas and not at graphs, we have to figure out from scratch what to compare an integral to.

• If we want to show that an integral converges, we have to find a larger function whose integral on the same interval converges.
• If we want to show that an integral diverges, we have to find a smaller function whose integral on the same interval diverges.

#### Example 1

 Let f (x) = e-x – 5. Doesconverge or diverge?

#### Example 2

 Let . Doesconverge or diverge?

#### Example 3

 Doesconverge or diverge?

#### Exercise 1

Determine if the integral converges or diverges. What integral are you using for comparison in each case?

#### Exercise 2

Determine if the integral converges or diverges. What integral are you using for comparison in each case?

#### Exercise 3

Determine if the integral converges or diverges. What integral are you using for comparison in each case?

#### Exercise 4

Determine if the integral converges or diverges. What integral are you using for comparison in each case?

#### Exercise 5

Determine if the integral converges or diverges. What integral are you using for comparison in each case?

#### Exercise 6

Determine if the integral converges or diverges. What integral are you using for comparison in each case?

#### Exercise 7

Determine if the integral converges or diverges. What integral are you using for comparison in each case?