1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 8.4 Improper Integrals

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 2 Quick Review

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 3 Quick Review

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 4 Quick Review Solutions

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 5 Quick Review Solutions

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 6 What you’ll learn about Infinite Limits of Integration Integrands with Infinite Discontinuities Test for Convergence and Divergence …and why The techniques of this section allow us to extend integration techniques to cases where the interval of integration [a,b] is not finite or where integrands are not continuous.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 7 Improper Integrals with Infinite Integration Limits

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 8 Example Evaluating an Improper Integral on [1,∞)

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 9 Example Using L’Hôpital’s Rule with Improper Integrals

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 10 Example Evaluating an Integral on (-∞,∞)

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 11 Improper Integrals with Infinite Discontinuities

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 12 Example Infinite Discontinuity at an Interior Point

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 13 Comparison Test

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 14 Example Finding the Volume of an Infinite Solid

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 15 Example Finding the Volume of an Infinite Solid

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 16 Quick Quiz Sections 8.3 and 8.4

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 17 Quick Quiz Sections 8.3 and 8.4

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 18 Quick Quiz Sections 8.3 and 8.4

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 19 Quick Quiz Sections 8.3 and 8.4

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 20 Quick Quiz Sections 8.3 and 8.4

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 21 Quick Quiz Sections 8.3 and 8.4

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 22 Chapter Test

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 23 Chapter Test

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 24 Chapter Test

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 25 Chapter Test

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 26 Chapter Test Solutions

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 27 Chapter Test Solutions

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 28 Chapter Test Solutions

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 29 Chapter Test Solution