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6 2 Notes 6 2 Notes Presentation Transcript

  • 6.2 Integration By Parts Goal: to integrate functions that are products
    Product Rule
    Let f(x) and g(x) be a differentiable functions of x
  • Integrate by Parts:
    OR
  • We need to figure out:
    • which factor is the easier factor to take the derivative of (u or f(x))
    and
    • which one is easier to integrate (dv or g’(x))
  • Guidelines:
    • Let u have a derivative simpler than itself (like a general power rule derivative)
    • Let dv be the most complex function that fits a basic integration formula (like ex)
    • Most common uses of integration by parts:
    • 1
    • 2
    • Most common uses of integration by parts:
    • 3
    • 4
  • Examples: