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8.4 Improper Integrals.

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Presentation on theme: "8.4 Improper Integrals."— Presentation transcript:

1 8.4 Improper Integrals

2 Quick Review

3 Quick Review

4 Quick Review Solutions

5 Quick Review Solutions

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 Improper Integrals with Infinite Integration Limits

8 Example Evaluating an Improper Integral on [1,∞)

9 Example Using L’Hôpital’s Rule with Improper Integrals

10 Example Evaluating an Integral on (-∞,∞)

11 Improper Integrals with Infinite Discontinuities

12 Example Infinite Discontinuity at an Interior Point

13 Comparison Test

14 Example Finding the Volume of an Infinite Solid

15 Example Finding the Volume of an Infinite Solid

16 Quick Quiz Sections 8.3 and 8.4

17 Quick Quiz Sections 8.3 and 8.4

18 Quick Quiz Sections 8.3 and 8.4

19 Quick Quiz Sections 8.3 and 8.4

20 Quick Quiz Sections 8.3 and 8.4

21 Quick Quiz Sections 8.3 and 8.4

22 Chapter Test

23 Chapter Test

24 Chapter Test

25 Chapter Test

26 Chapter Test Solutions

27 Chapter Test Solutions

28 Chapter Test Solutions

29 Chapter Test Solution


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