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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
Proof with u-v
Proof / Formula Integration by parts In words: First * Second minus of Second * D (first )
Integration by parts : worked out In words: First * Second minus of Second * D (first )
Illustration: Choosing u and dv L I P E T L Logarithmic I Inverse Trig P Polynomial E Exponential T Trig Let u be the first function from the mnemonic.
Illustration: u = dv = du = v =
Examples: (hidden product)
Examples: ( hidden product - ln ) LEARN IT !, LOVE IT !, LIVE IT ! Write it on your Anti-derivative page.
Chart: Short Cut for Algebraic + _ + _
Examples: (shortcut for algebraic u)
Examples: (Solve like an equation )
S. O. B. Problem Creativity is ALWAYS the Main Ingredient!
Last Update: 03/08/12 Assignment: p. 346 # 1 – 29 odd
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