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Generalizing the relation between H(x), F(x) and G(x)

  1. Apr 8, 2015 #1
    If [itex]H(x)= \int_c^x h(x)dx[/itex] and [itex]H(a) = F(a) - G(a) = \int_c^a h(x)dx[/itex] and [itex]H(b) = F(b) - G(b) = \int_c^b h(x)dx[/itex], then does that mean [itex]H(x) = F(x) - G(x)[/itex]? Is the information provided sufficient enough to come to that conclusion?
     
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  3. Apr 8, 2015 #2

    Simon Bridge

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    Can you come up with a sample F and G so that H=F-G holds for x=a and x=b but does not hold in general?
     
  4. Apr 8, 2015 #3
    No, H = F-G holds only for x = a and x = b. There isn't any information for any x other than a or b.
     
  5. Apr 8, 2015 #4

    Simon Bridge

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    Then you seem to have answered your own question.
     
  6. Apr 8, 2015 #5
    Haha..yeah..I think I have,
     
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