Integration Theorems

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Integration Theorems

• And Properties

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Integration Properties
b
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The average of a function

• How would you define the average of f on a,
  b ?
• How would you add up all the values of f on a,
  b ?

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The average of a function

• Using an algebraic trick, we can multiply and
  divide by (b a)

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Mean Value Theorem

• If f is continuous on a, b, then there exists a
  c ?a, b such that
• or

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Chain Rule

• By the definition of indefinite integral we know
  if
• F(x)
• Then
• dF(x) f(x)
• dx

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Chain Rule

• Therefore,
• f(g(x))

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Chain Rule

• Example

dx
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Examples