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

Slides:



Advertisements
Similar presentations
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Modeling and Optimization Section 4.4.
Advertisements

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Trapezoidal Rule Section 5.5.
Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
© 2010 Pearson Education, Inc. All rights reserved.
Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc. Chapter 13 The Trigonometric Functions Copyright © 2008 Pearson Education, Inc.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 1.
© 2010 Pearson Education, Inc. All rights reserved.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.2 Right Triangle Trigonometry.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Extreme Values of Functions Section 4.1.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivatives of Exponential and Logarithmic Functions Section 3.9.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Chain Rule Section 3.6.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 4.3 Connecting f ’ and f ” with the graph of f.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Antiderivatives and Slope Fields Section 6.1.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Linearization and Newton’s Method Section 4.5.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 8.2 L’Hôpital’s Rule.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Fundamental Theorem of Calculus Section 5.4.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 1 Functions.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.9 Derivatives of Exponential and Logarithmic Functions.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 3 Integration.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Rules for Differentiation Section 3.3.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 7.4 Lengths of Curves.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 6.3 Antidifferentiation by Parts.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.3 Product and Quotient Rules for Differentiation.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 8.4 Improper Integrals.
CHAPTER 6: DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELING SECTION 6.2: ANTIDIFFERENTIATION BY SUBSTITUTION AP CALCULUS AB.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivatives of Trigonometric Functions Section 3.5.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.1 Rates of Change and Limits.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 6.5 Logistic Growth.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Chapter 5 Integration.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 5.5 Trapezoidal Rule.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Areas in the Plane Section 7.2.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 1.3 Complex Numbers Quadratic Equations in the Complex Number System.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Integral As Net Change Section 7.1.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 6.4 Logarithmic Functions.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 6.5 Logistic Growth.
6.2 Antidifferentiation by Substitution Quick Review.
The Inverse Trigonometric Functions (Continued)
Sinusoidal Curve Fitting
4.5 Integration by Substitution
Section 9.1 Polar Coordinates
Section R.8 nth Roots; Rational Exponents
Building Exponential, Logarithmic, and Logistic Models from Data
Integration Techniques
Section 2.4 Circles Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Section 8.3 The Law of Cosines
Section 11.8 Linear Programming
Copyright © 2008 Pearson Prentice Hall Inc.
Copyright © 2008 Pearson Prentice Hall Inc.
Exponential Equations
Right Triangle Trigonometry; Applications
Mathematical Models: Building Functions
Copyright © 2008 Pearson Prentice Hall Inc.
Integration Techniques: Substitution
Integration Techniques: Substitution
Copyright © 2008 Pearson Prentice Hall Inc.
Right Triangle Trigonometry; Applications
Chapter 1 Functions Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Partial Fraction Decomposition
Right Triangle Trigonometry; Applications
Sinusoidal Curve Fitting
Quadratic Equations in the Complex Number System
Integration by Substitution (4.5)
Partial Fraction Decomposition
Properties of Rational Functions
Techniques of Integration
Antidifferentiation by Substitution
Copyright © 2008 Pearson Prentice Hall Inc.
Copyright © 2008 Pearson Prentice Hall Inc.
The Inverse Trigonometric Functions (Continued)
Presentation transcript:

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