Section 5.4 Theorems About Definite Integrals

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Section 5.4Theorems About Definite Integrals
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• Properties of Limits of Integration
• If a, b, and c are any numbers and f is a
  continuous function, then

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• Properties of Sums and Constant Multiples of the
  Integrand
• Let f and g be continuous functions and let c be
  a constant, then

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Example

• Given that
• find the following

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• The Area Between Two Curves
• If the graph of f(x) lies above the graph of g(x)
  on a,b, then

Area between f and g on a,b
Lets see why this works!
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• Using Symmetry to Evaluate Integrals
• An EVEN function is symmetric about the y-axis
• An ODD function is symmetric about the origin
• If f is EVEN, then
• If f is ODD, then

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EXAMPLE Given that Find
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Comparison of Definite Integrals

• Let f and g be continuous functions

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Example

• Explain why