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5044 Integration by Parts

5044 Integration by Parts. AP Calculus. Integration by Parts. Product Rules for Integration : A.    Is it a function times its derivative; u-du B.     Is it a function times the derivative of a second function; u- dv Integration by Parts. Proof with u-v : worked out.

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5044 Integration by Parts

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  1. 5044 Integration by Parts AP Calculus

  2. Integration by Parts • Product Rules for Integration : • A.    Is it a function times itsderivative; u-du • B.     Is it a function times the derivative of a secondfunction; u-dv • Integration by Parts

  3. Proof withu-v :worked out

  4. Proof with u-v

  5. Integration by parts Proof / Formula • In words: • First * Second minus of Second * D (first )

  6. Integration by parts : worked out In words: First * Second minus of Second * D (first )

  7. Illustration: Choosing u and dvL I P E T Let u be the first function from the mnemonic. L Logarithmic I  Inverse Trig P Polynomial E  Exponential T  Trig

  8. Illustration: u = dv = du = v =

  9. Examples:

  10. Examples: (hidden product)

  11. Examples: ( hidden product - ln ) LEARN IT ! , LOVE IT !,LIVE IT ! Write it on your Anti-derivative page.

  12. Chart: Short Cut for Algebraic + _ + _

  13. Examples: (shortcut for algebraic u)

  14. Examples: (shortcut for algebraic u)

  15. Examples: (Solve like an equation)

  16. Examples: (Solve like an equation)

  17. S. O. B. Problem Creativity is ALWAYS the Main Ingredient!

  18. Last Update: • 03/08/12 • Assignment: p. 346 # 1 – 29 odd

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