Chapter 9 Section 9.4 Improper Integrals

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Presentation transcript:

Chapter 9 Section 9.4 Improper Integrals Sequences, L’Hopital’s Rule, and Improper Integrals Section 9.4 Improper Integrals

Quick Review

Quick Review

Quick Review Solutions

Quick Review Solutions

What you’ll learn about Improper integrals Horizontally improper integrals (infinite limits of integration) Vertically improper integrals (intervals with points of infinite discontinuity) Comparison tests for convergence and divergence of improper integrals …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.

Improper Integrals with Infinite Integration Limits

Example Evaluating an Improper Integral on [1,∞)

Example Using L’Hôpital’s Rule with Improper Integrals

Example Evaluating an Integral on (– ∞,∞)

Improper Integrals with Infinite Discontinuities

Example Infinite Discontinuity at an Interior Point

Comparison Test

Example Finding the Volume of an Infinite Solid

Example Finding the Volume of an Infinite Solid

Quick Quiz Sections 9.3 and 9.4

Quick Quiz Sections 9.3 and 9.4

Quick Quiz Sections 9.3 and 9.4

Quick Quiz Sections 9.3 and 9.4

Quick Quiz Sections 9.3 and 9.4

Quick Quiz Sections 9.3 and 9.4

Chapter Test

Chapter Test

Chapter Test

Chapter Test

Chapter Test Solutions

Chapter Test Solutions

Chapter Test Solutions

Chapter Test Solution

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