Section 5.4 Theorems About Definite Integrals

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Section 5.4 Theorems About Definite Integrals

Properties of Limits of Integration If a, b, and c are any numbers and f is a continuous function, then

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

Example Given that find the following:

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!

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

EXAMPLE Given that Find

Comparison of Definite Integrals Let f and g be continuous functions

Example Explain why