Chapter 4.5 - Integration by Substitution

Objectives:

• • Use pattern recognition to evaluate an indefinite integral.

  • Use a change of variables to evaluate an indefinite integral.

  • Use the General Power Rule for Integration to evaluate an indefinite integral.

  • Use a change of variables to evaluate a definite integral.

  • Evaluate a definite integral involving an even or odd function.

Recognizing the f(g(x))g'(x) pattern, or "Unchaining" (for Day #45 lesson)

The Chain Rule produced a particular pattern during the differentiation process. We need to learn to recognize the f(g(x))g'(x) pattern so that we may "unchain" during the antidifferentiation process.

U-Substitution (Integration by Substitution) pt1 (for Day #46 lesson)

Using u-substitution (a.k.a. integration by substitution) on indefinite integrals. This process is your next resort when "unchaining" doesn't work.

Here is first custom example from class, and here are the two “Now you try” solutions.

U-Substitution (Integration by Substitution) pt2 (for Day #47 lesson)

Using u-substitution (a.k.a. integration by substitution) on definite integrals. For definite integrals, a shortcut may be used to save you a little time.

Format/Topics of Chapter 4.5 Assessment

15 Multiple Choice

• • All topics are fair game, as usual

6 Short Answer

• • Average Value and Mean Value Theorem for Integrals

  • Second FTC

  • Integration by "Unchaining"

  • Integration by U-Substitution (Definite and Indefinite)

  • Trig antiderivatives