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Continuity of one function, implies continuity of another?

  1. Feb 16, 2014 #1
    Hi

    Lets say that f(x) is continuous. Then [itex] \int_0^x \! f(t)dt=G(x)[/itex] is continuous. (I don't think you have to say that f need to be continuous for this, all we need to say is that f is integrable?, or do we need continuity of f here?)

    But my main question is about the converse. lets say that [itex] \int_0^x \! f(t)dt=G(x)[/itex] is continuous, does that imply that f is continuous?

    Have a nice sunday.
     
    Last edited: Feb 16, 2014
  2. jcsd
  3. Feb 16, 2014 #2

    pasmith

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    This is true for any integrable function.

    No: by the above, [itex]f[/itex] does not need to be continuous for its integral to be continuous.
     
  4. Feb 16, 2014 #3
    Hehe, ofcourse, thanks.
     
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