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MAT 1221 Survey of Calculus

MAT 1221 Survey of Calculus. Section 7.1 Integration by Parts. http://myhome.spu.edu/lauw. Expectations. Simplify the answer. 6 minutes. Preview. The reverse of the product rule. Derivatives and Antiderivatives. Product Rule. Definition of Antiderivatives.

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MAT 1221 Survey of Calculus

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

  2. Expectations • Simplify the answer. • 6 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 Easier Difficult The formula is useful if the integral on the right hand side is easier to evaluate than the one on the left hand side

  9. Alternative Form

  10. Integration By Parts

  11. Example 1

  12. Example 1 In order to use IBP, we need to choose the functions and . One possible choice is

  13. Example 1 Now, we need to find and

  14. Remarks 1. In the step of finding v, we always omit the arbitrary constant. Such a constant does not affect the final form of the answer.

  15. Remarks 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

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