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Homework Help: Riemann integrability

  1. Dec 18, 2017 #1
    1. The problem statement, all variables and given/known data
    Find a such that f is Riemann integrable on [0,1], where:
    ##f = x^acos(1/x)##, x>0 and f(0) = 0

    2. Relevant equations

    3. The attempt at a solution
    I found at previous points a such that f is continuous, bounded and derivable, but I am not sure how to use that (as all these implications work just one way). Also the definition with partitions seems hard to use here. Any hint?
    Last edited by a moderator: Dec 19, 2017
  2. jcsd
  3. Dec 19, 2017 #2


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    2017 Award

    Staff: Mentor

    You should have a statement "a function is Riemann integrable if it is [...]" that helps with all a where it is integrable. For the rest you'll have to see how to show that it is not.
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