1. MAT 1221 Survey of Calculus Section 7.1 Integration by Parts http://myhome.spu.edu/lauw

2. Expectations Show all the steps Simplify the answer. 7 minutes

3. Preview The reverse of the product rule

4. Derivatives and Antiderivatives

5. Product Rule

6. Definition of Antiderivatives

7. By Definition of Antiderivatives

8. Rationale The formula is useful if the integral on the right hand side is easier to evaluate than the one on the left hand side Easier Difficult

9. Alternative Form

10. Integration By Parts

11. Example 1

14. Remarks

15. 2. If we make a different choice such as

16. Example 2

17. Example 3

18. Additional Formula To make calculations a bit easier, we are going to adopt the following new formula

19. Example 4

20. Remarks Do not use IBP for all integrals. Sometimes, Substitution is easier.

21. Example 5

22. Next Class Session Learn how to use a CAS (Computer Algebra System) - Maple