Explore BrainMass

Explore BrainMass

    Real Analysis: Riemann Integrability

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Please see the attached file for the fully formatted problem.

    Let E = { 1/n : n 2 N } . Prove that the function
    f(x) =
    ?
    1 x 2 E
    0 otherwise
    is integrable on [0,1]. What is the value of
    R
    1
    0 f(x)dx?
    Since this problem is an analysis problem, please be sure to be rigorous.
    It falls under the chapter on Integrability on R , where they define partition,
    refinement of a partition, upper and lower Riemann sums, (Riemann)
    integrability, and upper and lower integrals in terms of the infimum and
    supremum of the respective sums.
    1

    © BrainMass Inc. brainmass.com November 29, 2021, 11:55 pm ad1c9bdddf
    https://brainmass.com/math/real-analysis/real-analysis-riemann-integrability-9711

    Attachments

    Solution Summary

    A function is proven to be Riemann integrable. The solution is detailed and well presented.

    $2.49

    ADVERTISEMENT