Integration by parts
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AP Calculus BC Integration By Parts
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Transcript of Integration by parts
AP Calculus BC
Integration By Parts
Integration By Parts
• FDWK 6.3, Larson 7.2• Basic Formula: • Integration counterpart of the product rule for
derivatives• Also used to find the integrals of logarithmic
and inverse trigonometric functions• Works with indefinite and definite integrals as
well
Examples
• Deriving the formula• Integration by Parts for Indefinite Integrals• Integration by Parts for Definite Integrals• Repeated Integration by Parts• Solving for the Unknown Integral• Tabular Integration by Parts• Integrals of Logarithmic Functions • Integrals of Inverse Trigonometric Functions
Integration By Parts for Indefinite Integrals
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Integration by Parts for Definite Integrals
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Wrapping it Up
• When to use Integration by Parts?– When you have a product that cannot be
simplified and substitution doesn’t apply– It often involves a product of polynomial functions
with exponential or trig functions, or just exponential and trig functions
– It can be used to find the integrals of logarithmic functions
– It can be used to find the integrals of inverse trig functions
