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# Calculus II - 3

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Stewart Calculus Section 7.3

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• ### Calculus II - 3

1. 1. 7.3 Trigonometric Substitution
2. 2. 7.3 Trigonometric SubstitutionTwo Kinds of substitutions ( ( )) ( ) = ( )
3. 3. 7.3 Trigonometric SubstitutionTwo Kinds of substitutions ( ( )) ( ) = ( )Ex1: =
4. 4. 7.3 Trigonometric SubstitutionTwo Kinds of substitutions ( ( )) ( ) = ( )Ex1: = =
5. 5. 7.3 Trigonometric SubstitutionTwo Kinds of substitutions ( ( )) ( ) = ( )Ex1: = =Ex2: = ·
6. 6. 7.3 Trigonometric SubstitutionTwo Kinds of substitutions ( ( )) ( ) = ( )Ex1: = =Ex2: = · = − ≤ ≤
7. 7. 7.3 Trigonometric SubstitutionTwo Kinds of substitutions ( ( )) ( ) = ( )Ex1: = =Ex2: = · = = − ≤ ≤
8. 8. Expression Substitution Identity √ = − − = − ≤ ≤ √ = + + = − < < √ = − − = ≤ <
9. 9. (0,b)Ex: Find the area. O (a,0)
10. 10. (0,b)Ex: Find the area. O (a,0) √ = −
11. 11. (0,b)Ex: Find the area. O (a,0) √ = − = = ≤ ≤
12. 12. (0,b)Ex: Find the area. O (a,0) √ = − = = ≤ ≤ = ( + )
13. 13. (0,b)Ex: Find the area. O (a,0) √ = − = = ≤ ≤ = ( + ) =[ + ] =
14. 14. Ex: Find
15. 15. Ex: Find = = − ≤ ≤
16. 16. Ex: Find = = − ≤ ≤ = ( )
17. 17. Ex: Find = = − ≤ ≤ = ( ) = +
18. 18. Ex: Find = = − ≤ ≤ = ( ) = + = +
19. 19. Ex: Find
20. 20. Ex: Find √ = = < <
21. 21. Ex: Find √ = = < < = | + |+
22. 22. Ex: Find √ = = < < = | + |+ = + +
23. 23. Ex: Find √ = = < < = | + |+ = + + = + +
24. 24. Ex: Find +
25. 25. Ex: Find + = − < = < + ·
26. 26. Ex: Find + = − < = < + · =
27. 27. Ex: Find + = − < = < + · = = =
28. 28. Ex: Find + = − < = < + · = = = = +
29. 29. Ex: Find + = − < = < + · = = = = + + = +
30. 30. Ex: Find
31. 31. Ex: Find = = +
32. 32. Ex: Find = = + = ( )( ) =− < <
33. 33. Ex: Find = = + = ( )( ) =− < < = +
34. 34. Ex: Find = = + = ( )( ) =− < < = + = +
35. 35. Ex: Find = = + = ( )( ) =− < < = + = + + = +