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

  • Thread starter andyrk
  • Start date
  • #1
andyrk
658
5
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?
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,874
1,657
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
andyrk
658
5
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
Science Advisor
Homework Helper
17,874
1,657
Then you seem to have answered your own question.
 
  • #5
andyrk
658
5
Haha..yeah..I think I have,
 

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

Replies
11
Views
630
  • Last Post
Replies
15
Views
821
Replies
24
Views
1K
  • Last Post
Replies
13
Views
1K
  • Last Post
Replies
8
Views
851
Replies
10
Views
1K
  • Last Post
Replies
6
Views
657
  • Last Post
Replies
1
Views
344
  • Last Post
Replies
4
Views
524
Top