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CHAPTER 2

CHAPTER 2. Integration by Parts. 2.4 Continuity. The formula for integration by parts  f ( x ) g’ ( x ) dx = f ( x ) g(x) -  g ( x ) f’ ( x ) dx. Substitution Rule that is easy to remember

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CHAPTER 2

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  1. CHAPTER 2 Integration by Parts 2.4 Continuity The formula for integration by parts  f (x) g’(x) dx = f (x) g(x) -  g(x) f’(x) dx . Substitution Rule that is easy to remember Let u = f (x) and v = g(x). Then the differentials are du = f’(x) dx and dv = g’(x) dx and the formula is:  udv = u v -  vdu .

  2. Example: Find x cos x dx. Example: Evaluate  t2 et dt. abf (x) g’(x) dx = [f (x) g(x)]ab-ab g(x)f ’(x) dx. Example: Evaluate 01 tan-1x dx. Example: Evaluate  x ln x dx. Example: Evaluate  (2x + 3)ex dx.

  3. abf (x) g’(x) dx = [f (x) g(x)]ab-ab g(x)f ’(x) dx. Example: Evaluate 01 tan-1x dx. Example: Evaluate 1ex ln x dx. Example: Evaluate 01(2x + 3)ex dx.

  4. CHAPTER 2 Integration Using Technology and Tables 2.4 Continuity Example: Use the Table of Integrals to find: 1.  x2 cos 3x dx. 2.  [(4 - 3x2)0.5/x ] dx. 3.  e sin x sin 2x dx.

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