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Techniques of Integration
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  Lecture 9 - Techniques of Integration AMA140/150 Calculus AMA140/150 Calculus Lecture 9 - Techniques of Integration  Outline Properties of indefinite integralsIntegration by substitutionIntegration by partsReduction FormulaMethod of Partial Fractions AMA140/150 Calculus Lecture 9 - Techniques of Integration  Properties of indefinite integrals Properties of definite integralsFor  a ,  b  , and  c   are real numbers, 1    cf     x   dx     c     f     x   dx  ; 2     f     x   ± g   x   dx       f     x   dx   ±    g   x   dx  . AMA140/150 Calculus Lecture 9 - Techniques of Integration  Integration by substitution Integration by substitutionIf   u     u   x    is a differentiable function and  f    is continuous, then    g   u   du dx  dx       g   u   u    x   dx       g   u   du  . We can preform the method of integration by substitution as follows: 1  Write the integral as the form    f     x   dx       g   u   du dx  dx  , for some “inside function”  u     u   x   . 2  Then  du     du dx  dx   and so    f     x   dx       g   u   du  . Therefore, we can evaluate the latter integral instead. AMA140/150 Calculus Lecture 9 - Techniques of Integration
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