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Math Help - proof

  1. #1
    Newbie
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    proof

    Let f be an integrable function on [a,b]. Suppose that f(x)≥0 for all x and there is at least one point x_{0} ∈ [a,b] at which f is continuous and strictly positive. Show that
    b
    \int f(x)dx>0
    a

    I think I am missing something because it looks too simple, since the function is continuous and strictly positive doesn't the integral have to be >0?
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  2. #2
    Senior Member Tinyboss's Avatar
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    Yes it does, but that's exactly what you have to show. How you gonna do it?
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  3. #3
    MHF Contributor

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    Note, however, that the problem does NOT say that f is continous on [a, b], only that it is continuous at x_0. But you can show from that there exist some interval around x_0 in which f is continous and positive. The integral over that interval is positive and f is never negative.
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