Basic Integration Rules - PowerPoint PPT Presentation


Title: Basic Integration Rules


1
Basic IntegrationRules
  • Lesson 8.1

2
Fitting Integrals to Basic Rules
  • Consider these similar integrals
  • Which one uses
  • The log rule
  • The arctangent rule
  • The rewrite with long division principle

3
Try It Out
  • Decide which principle to apply

4
The Log Rule in Disguise
  • Consider
  • The quotient suggests possible Log Rule, but the
    du ex is not present
  • We can manipulate this to make the Log Rule apply
  • Add and subtract ex in the numerator

5
The Power Rule in Disguise
  • Here's another integral that doesn't seem to fit
    the basic options
  • What are the options for u ?
  • Best choice is

6
The Power Rule in Disguise
  • Thenbecomes and power rule
    applies
  • Note review of basic integration rules pg 520
  • Note procedures for fitting integrands to basic
    rules, pg 521

7
Disguises with Trig Identities
  • What rules might this fit?
  • Note that tan2 u is not on the list
  • However sec2u is on the list
  • This suggests one of the pythagorean identities
    and we have

8
Assignment
  • Lesson 8.1
  • Page 522
  • Exercises 1 49 EOO
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Basic Integration Rules

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Basic Integration Rules Lesson 8.1 Fitting Integrals to Basic Rules Consider these similar integrals Which one uses The log rule The arctangent rule The rewrite ... – PowerPoint PPT presentation

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Title: Basic Integration Rules


1
Basic IntegrationRules
  • Lesson 8.1

2
Fitting Integrals to Basic Rules
  • Consider these similar integrals
  • Which one uses
  • The log rule
  • The arctangent rule
  • The rewrite with long division principle

3
Try It Out
  • Decide which principle to apply

4
The Log Rule in Disguise
  • Consider
  • The quotient suggests possible Log Rule, but the
    du ex is not present
  • We can manipulate this to make the Log Rule apply
  • Add and subtract ex in the numerator

5
The Power Rule in Disguise
  • Here's another integral that doesn't seem to fit
    the basic options
  • What are the options for u ?
  • Best choice is

6
The Power Rule in Disguise
  • Thenbecomes and power rule
    applies
  • Note review of basic integration rules pg 520
  • Note procedures for fitting integrands to basic
    rules, pg 521

7
Disguises with Trig Identities
  • What rules might this fit?
  • Note that tan2 u is not on the list
  • However sec2u is on the list
  • This suggests one of the pythagorean identities
    and we have

8
Assignment
  • Lesson 8.1
  • Page 522
  • Exercises 1 49 EOO
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