5.5 The Substitution Rule

1-3.Evaluate the given indefinite integral using am appropriate substitution.

1. .

 ,

      .

2. .

 ,

3. .

,

      .

4-10. Find the indefinite integral.

4. .

.

5. .

 .

6. .

 .       

7. ..

8. ..

     ,

                         .

9. .       

 .

10. .

  .

11-23. Evaluate the definite integral, if it exists.

11. .

.      (Because is odd function)

12. .

 .

13. .

      .

14. .

 .

15. .     

 4.

16. .

      ,

      .

17. .      

 ,

18. .

 Since

      ,

      first we have

      Then,

      (Because is even function.)

      Hence

19. .

  because is odd function.

20. .

 .

21. .

 .

22. .

 .

23. .

  because is odd function.

24-25. Find the exact area.

24. , .

 .

25. , .

 4

26. Let be a function symmetrical with respect to .

Show , when .

 Since

      .

      Hence .

         because is a function symmetrical with respect to .