# 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 converge or diverge? |

#### Example 2

Let . Does converge or diverge? |

#### Example 3

Does converge or diverge? |

#### Example 4

Does converge 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

(hint: for *x* > 1, we know sin *x* < *x* and )