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Math Help - integral hard Q s

  1. #1
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    integral hard Q s

    Let f(x) = x^(1/2) on the interval [0, 1]. Show from the definition that f is integrable on [0, 1].

    Using the partition
    x =(i/n)^2 , i = 0, 1, . . . n.
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  2. #2
    Senior Member vincisonfire's Avatar
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    We usually use Riemann sums to define the integral. This require the existence of the function over [0,1] and the continuity of it over ]0,1[.
    Show that and I think it will be sufficient.
    First part is easily checked.
    For second part, show that there is a discontinuity at 0. It follows that the set is open (since infinity is not included) and it is therefore continuous over ]0,1[.
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  3. #3
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    hi can you please prove this as i am unable to find
    with thanks
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