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Thread: Examples of Riemann integrable functions

  1. #1
    Member thaopanda's Avatar
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    Examples of Riemann integrable functions

    I'm no good at coming up with examples... please help...

    a. Give an example of a function f: [0,2] \rightarrow R such that f isn't Riemann integrable on [0,2], but |f| is.

    b. Give an example of a function f: [0,2] \rightarrow R such that f isn't Riemann integrable on [0,2], but f^2 is.

    c. Give an example of two functions f,g : [0,1] \rightarrow R such that f is Riemann integrable on [0,1], but g isn't and fg is Riemann integrable on [0,1].
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  2. #2
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    Let f(x)= 1 if x\in \mathbb{Q} and f(x)=-1 if x\in \mathbb{R} \setminus \mathbb{Q} and g\equiv 0
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  3. #3
    Member thaopanda's Avatar
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    wouldn't g be the one that's integrable in that case? I assume I would just swap the f(x) and the g(x)
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