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    Riemann integrable

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    Let f_n(x)= (sin(1/x))^n when x does not equal zero and f_n(x)=0 when x = 0 .

    a. Show that f_n(x) is Riemann integrable.

    b. Calculate lim(as n goes to infinity) integral ( from 0 to 1) f_n(x)dx .

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    if ;
    (a) I claim that is Riemann Integrable on
    For any , we note that is continuous on and thus is Riemann integrable on . So we can find a partition on , such that , ...

    Solution Summary

    Riemann integrable is evaluated in this solution.