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Mean Value Theorem

Learn how the Mean Value Theorem for Definite Integrals guarantees an average value equal to the actual value of a continuous function. Explore examples with f(x) = x^2 and f(x) = sin(x).

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Mean Value Theorem

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  1. Mean Value Theorem 4.4b

  2. Mean Value Theorem (for definite integrals) If f is continuous on then at some point c in , The mean value theorem for definite integrals says that for a continuous function, at some point on the interval the actual value will equal the average value. p

  3. The average value of a function is the value that would give the same area if the function was a constant:

  4. Example • Find the average value and the “c” guaranteed by the MVTI of f(x) = x2 on the interval [2, 4]

  5. Example • Find the average value of f(x) = sin x

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