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Math Help - Mean Value Theorem for Integrals

  1. #1
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    Mean Value Theorem for Integrals

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  2. #2
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    Since f is continous it attains its maximum and minimum.
    This means there are k_1,k_2 so that f(k_1)\leq f(x)\leq f(k_2).
    Since g(x)\geq 0 multiplication does not reverse inequality, f(k_1)g(x)\leq f(x)g(x)\leq f(k_2)g(x).
    Now integrate both sides, this is possible since g is continous.
    And finally the last statement follows by indetermediate value theorem for continous functions.
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