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Calculating Average Function Value of f on an Interval

Learn how to find the average value of a function f(x) on a specified interval [a, b] using the Mean Value Theorem for Integrals, with examples and exercises. Find the average value and discover the point c where f(c) equals the average value.

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Calculating Average Function Value of f on an Interval

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  1. 6.5 Average Value of a Function

  2. The Average Value of f on the interval [a, b]:

  3. Ex 1: Find the average value of f(x) on the interval [0, /4]:

  4. MVT for Integrals: If f is continuous on [a, b], then  a # c in [a, b] such that

  5. Ex 2: Find c in [0, 2] such that fave = f (c).

  6. Ex 3: Find the numbers b such that the average value of f(x) in [0, b] is equal to 3.

  7. HW: 6.5 pg. 462# 1 – 15 odds

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