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SECTION 5.5 (AND 5.7) Integration by Substitution & Natural Logs

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Section 5.5 (and 5.7). Integration by Substitution & Natural Logs. The Chain Rule & Integration. How do we handle something like this? Think back to how we took the derivative of a composite function like. -Substitution. Example 1. - PowerPoint PPT Presentation

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Page 1: Section 5.5 (and 5.7)

SECTION 5.5 (AND 5.7)

Integration by Substitution & Natural Logs

Page 2: Section 5.5 (and 5.7)

The Chain Rule & Integration• How do we handle something like this?

• Think back to how we took the derivative of a composite function like . . .

Page 3: Section 5.5 (and 5.7)

-Substitution

Page 4: Section 5.5 (and 5.7)

Example 1Find the indefinite integral and check the result by differentiation.

Page 5: Section 5.5 (and 5.7)

Example 2Find the indefinite integral and check the result by differentiation.

Page 6: Section 5.5 (and 5.7)

Example 3Find the indefinite integral and check the result by differentiation.

Page 7: Section 5.5 (and 5.7)

What about some of our other trig fnc.’s?• Can we use some of these methods to integrate

something like what we have below?

Page 8: Section 5.5 (and 5.7)

What about some of our other trig fnc.’s?• Can we use some of these methods to integrate

something like what we have below?

Page 9: Section 5.5 (and 5.7)
Page 10: Section 5.5 (and 5.7)

Example 4Find the indefinite integral and check the result by differentiation.

Page 11: Section 5.5 (and 5.7)

Example 5Find the indefinite integral and check the result by differentiation.

Page 12: Section 5.5 (and 5.7)

Example 6Find the indefinite integral and check the result by differentiation.

Page 13: Section 5.5 (and 5.7)

Example 7Find the indefinite integral and check the result by differentiation.

Page 14: Section 5.5 (and 5.7)

Example 8Find the indefinite integral and check the result by differentiation.

Page 15: Section 5.5 (and 5.7)

Example 9Find the indefinite integral and check the result by differentiation.

Page 16: Section 5.5 (and 5.7)

Example 10Evaluate the definite integral.

Page 17: Section 5.5 (and 5.7)

Example 11Evaluate the definite integral.


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