Integration by parts

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  • try to check back on page 6,there is wrong substitution happen on this equation where supposelyV=-e^(-x)
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Integration by parts

  1. 1. AP Calculus BC<br />Integration By Parts<br />
  2. 2. Integration By Parts<br />FDWK 6.3, Larson 7.2<br />Basic Formula: 𝑒 𝑑𝑣=π‘’π‘£βˆ’π‘£Β π‘‘π‘’<br />Integration counterpart of the product rule for derivatives<br />Also used to find the integrals of logarithmic and inverse trigonometric functions<br />Works with indefinite and definite integrals as well<br />Β <br />
  3. 3. Examples<br />Deriving the formula<br />Integration by Parts for Indefinite Integrals<br />Integration by Parts for Definite Integrals<br />Repeated Integration by Parts<br />Solving for the Unknown Integral<br />Tabular Integration by Parts<br />Integrals of Logarithmic Functions <br />Integrals of Inverse Trigonometric Functions<br />
  4. 4. Deriving the Formula 𝑒 𝑑𝑣=π‘’π‘£βˆ’π‘£Β π‘‘π‘’<br />Β <br />Click here for video<br />
  5. 5. Integration By Parts for Indefinite Integrals<br />Click here for video<br />
  6. 6. Integration by Parts for Definite Integrals<br />Click here for video<br />
  7. 7. Repeated Integration By Parts<br />Click here for video<br />
  8. 8. Solving for the Unknown Integral<br />Click here for video<br />
  9. 9. Tabular Integration by Parts<br />Click here for video<br />
  10. 10. Integrals of Logarithmic Functions<br />Click here for video<br />
  11. 11. Integrals of Inverse Trig Functions<br />Click here for video<br />
  12. 12. Wrapping it Up<br />When to use Integration by Parts?<br />When you have a product that cannot be simplified and substitution doesn’t apply<br />It often involves a product of polynomial functions with exponential or trig functions, or just exponential and trig functions<br />It can be used to find the integrals of logarithmic functions<br />It can be used to find the integrals of inverse trig functions<br />

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