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

  • Thread starter andyrk
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  • #1
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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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  • #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?
 
  • #3
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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?
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.
 
  • #4
Simon Bridge
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Then you seem to have answered your own question.
 
  • #5
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Haha..yeah..I think I have,
 

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