Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Continuity of one function, implies continuity of another?

  1. Feb 16, 2014 #1

    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


    User Avatar
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook