# 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