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Section 5.4 Theorems 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] Let’s 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
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