Prove the mean value theorem for integrals. That is, prove that if f : [a, b] ? ? is continuous, then there exists a c ? [a, b] such that ?[a,b] f = f(c)(b - a).
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We know that f is continuous on [a, b], so by the Extreme Value Theorem, f has a maximum and a minimum on [a, b]. Let M and m be the maximum and minimum values of f on [a, b], respectively. Show more…
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