1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Integration by Substitution Section 6.2

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 2 What you’ll learn about Substitution in Indefinite Integrals Substitution in Definite Integrals … and why Antidifferentiation techniques were historically crucial for applying the results of calculus.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 3 Power Functions

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 4 Trigonometric Formulas

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 5 Exponential and Logarithmic Formulas

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 6 Example Paying Attention to the Differential

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall The Substitution Method Used to integrate composite functions Substitute u = g(x) and du = g’(x)dx to obtain the integral Integrate with respect to u. Replace u with g(x) in the result. Slide 6- 7

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 8 Example Using Substitution

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 9 Example Using Substitution

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 10 Example Setting Up a Substitution with a Trigonometric Identity

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall The Substitution Method (Definite Integrals) Slide 6- 11

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 12 Example Evaluating a Definite Integral by Substitution

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 13 Example Evaluating a Definite Integral by Substitution

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Pages 321-322 (1-27 odd, 31-37 odd) Slide 6- 14