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    Real Analysis of Criteria for Integrability

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    Suppose that the function f:[a,b]->R is integrable and there is a postive number m such that f(x) >= m for all x in [a,b]. Show that the reciprocal function 1/f:[a,b]->R is integrable by proving that for each partition P of the interval [a,b],

    U(1/f,P) - L(1/f,P) <= 1/m^2[U(f,P) - L(f,P)]

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    Solution Summary

    The reciprocal of a function is shown to be integrable using partitions.
    The solution is detailed and well presented.