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

[andyrk]

If H(x)= \int_c^x h(x)dx and H(a) = F(a) - G(a) = \int_c^a h(x)dx and H(b) = F(b) - G(b) = \int_c^b h(x)dx, then does that mean H(x) = F(x) - G(x)? Is the information provided sufficient enough to come to that conclusion?

 

[Simon Bridge]

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?

 

[andyrk]

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.

 

[Simon Bridge]

Then you seem to have answered your own question.

 

[andyrk]

Haha..yeah..I think I have,