Homework 13 Solution - Improper Integrals SUGGESTED REFERENCE MATERIAL As you work through the problems listed below you should reference Chapter 7.8 of

Homework 13 Solution - Improper Integrals SUGGESTED...

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Improper Integrals SUGGESTED REFERENCE MATERIAL: As you work through the problems listed below, you should reference Chapter 7.8 of the rec- ommended textbook (or the equivalent chapter in your alternative textbook/online resource) and your lecture notes. EXPECTED SKILLS: Given an improper integral, which either has an infinite interval of integration or an infinite discontinuity, be able to evaluate it using a limit. Know how to determine if such an integral converges (and if so, what it converges to) or diverges. PRACTICE PROBLEMS: For problems 1-13, evaluate each improper integral or show that it diverges. 1. Z 1 1 x dx 2. Z 3 -∞ 3 x x 2 + 1 dx -∞ 3. Z 1 e - x dx 1 e 4. Z 1 xe - 3 x 2 dx 1 6 e - 3 5. Z 4 0 1 x 2 / 3 dx 3 3 4 1

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