Mean Value Theorem 5.4.

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Presentation transcript:

Mean Value Theorem 5.4

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. Mean Value Theorem (for definite integrals) If f is continuous on then at some point c in , p

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

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

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