Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Integration by Substitution Section 6.2
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.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 3 Power Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 4 Trigonometric Formulas
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 5 Exponential and Logarithmic Formulas
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 6 Example Paying Attention to the Differential
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
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 8 Example Using Substitution
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 9 Example Using Substitution
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Setting Up a Substitution with a Trigonometric Identity
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall The Substitution Method (Definite Integrals) Slide 6- 11
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Evaluating a Definite Integral by Substitution
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Evaluating a Definite Integral by Substitution
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Pages (1-27 odd, odd) Slide 6- 14