section 5.5 (and 5.7)
DESCRIPTION
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 PresentationTRANSCRIPT
![Page 1: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/1.jpg)
SECTION 5.5 (AND 5.7)
Integration by Substitution & Natural Logs
![Page 2: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/2.jpg)
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)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/3.jpg)
-Substitution
![Page 4: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/4.jpg)
Example 1Find the indefinite integral and check the result by differentiation.
![Page 5: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/5.jpg)
Example 2Find the indefinite integral and check the result by differentiation.
![Page 6: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/6.jpg)
Example 3Find the indefinite integral and check the result by differentiation.
![Page 7: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/7.jpg)
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)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/8.jpg)
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)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/9.jpg)
![Page 10: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/10.jpg)
Example 4Find the indefinite integral and check the result by differentiation.
![Page 11: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/11.jpg)
Example 5Find the indefinite integral and check the result by differentiation.
![Page 12: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/12.jpg)
Example 6Find the indefinite integral and check the result by differentiation.
![Page 13: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/13.jpg)
Example 7Find the indefinite integral and check the result by differentiation.
![Page 14: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/14.jpg)
Example 8Find the indefinite integral and check the result by differentiation.
![Page 15: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/15.jpg)
Example 9Find the indefinite integral and check the result by differentiation.
![Page 16: Section 5.5 (and 5.7)](https://reader031.vdocument.in/reader031/viewer/2022020209/56813c27550346895da5a136/html5/thumbnails/16.jpg)
Example 10Evaluate the definite integral.
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Example 11Evaluate the definite integral.