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The Average Value of a FunctionWe can use the definite integral to find the average value of a function.Suppose f is an integrable function on the interval [a, b]. Then the average value of f over the interval is ∫−badxxfab)(1. This is what average value represents: Example 7: Find the average value of xxf=)( over the interval [1, 16]. Example 8: Find the average value of 53)(2+−=xxxfon [2, 5].
Example 9: The sales of ABC Company in the first t years of its operation is approximated by the function 2( )0.24S ttt=+where ( )S t is measured in millions of dollars. What were the company’s average annual sales over its first five years of operation? From this lesson, you should be able to Use the FTOC to compute definite integrals, including problems that require substitution Define average value Use the FTOC to find average value Solve word problems using FTOC
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