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Domain of an antiderivative

  1. Aug 16, 2015 #1
    Isn't the domain of the derivative of a function a subset of the domain of the function itself?
    Does this mean that the domain of an integrand is always a subset of the corresponding indefinite integral?
     
  2. jcsd
  3. Aug 16, 2015 #2
    We know that if a function ## g ## has a derivative ## h ##, then ##dom(h)\subseteq dom(g)##.

    Let ## f ## be our function and ## F ## be any of its corresponding antiderivatives. Then since ## F ## has a derivative ## f ##, it follows that ##dom(f)\subseteq dom(F)##.
     
  4. Aug 18, 2015 #3

    HallsofIvy

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    The domain of the derivative is always a subset of the domain of the function but not necessarily equal. for example, the function f(x)= |x| has domain "all real numbers" while it derivative, f'(x)= 1 if x> 0, -1 if x< 0, as domain "all real numbers except 0".
     
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