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Analysis 2- Riemann integrable functions

  1. Sep 7, 2010 #1
    1. If abs(f) is Riemann integrable on [a,b], then f is Riemann integrable on [a,b]. True or false (show work)

    2. A function f is Riem Int iff f is bounded on [a,b], and for every epsilon>0 there is a partition P of [a,b] s.t. U(f,P)-L(f,P)<epsilon

    3. I believe that this is true. So, what I want to do is show that f is bounded don [a,b], and I also want to show the second part of the definition. To show it was bounded, I used the fact that abs(f) was bounded and eventually got sup(abs(f))<=sup(f) and inf(f)>=-sup(abs(f)), which *I think* proved that f is bounded.

    My question is how do I show that it fits the second part of the definition?
  2. jcsd
  3. Sep 7, 2010 #2


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    You can't show the second part. Because it isn't true. Try to find a counterexample.
  4. Sep 7, 2010 #3
    I'm not sure what the question is and whats your answer. However the statement "if abs(f) is Riemann integrable on [a,b] then f is Riemann integrable on [a,b] isn't true."
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