If integral equal to zero, then?

  • #1

Homework Statement


if this statement is true:
[itex]\int_0^\infty f(x) dx= 0[/itex]
then is this true?
[itex] f(x) = 0[/itex] in domain [itex]x\in [0,\infty)[/itex]


Homework Equations


-NA-


The Attempt at a Solution


Hmm.. I can't come out with a formula that refute that. I would think of an odd function that changes sign in [itex]\infty/2[/itex], except it doesn't exist.

I would think it's false, but i need some example...
 

Answers and Replies

  • #2
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,796
1,670
What if f(x) = sin(x)?
 
  • #3
ehild
Homework Helper
15,543
1,912
What if f(x) = sin(x)?

Its improper integral is not defined.

ehild
 
  • #5
actually I think it might be er..
[itex] f(x)=sin(x)[/itex] for [itex]x=[0,2\pi][/itex]
[itex] f(x)=0[/itex] for others
 
  • #6
ehild
Homework Helper
15,543
1,912
That will do ...

ehild
 

Related Threads on If integral equal to zero, then?

Replies
17
Views
31K
  • Last Post
Replies
1
Views
854
Replies
4
Views
1K
Replies
24
Views
1K
  • Last Post
Replies
3
Views
4K
Replies
3
Views
4K
Replies
3
Views
6K
Replies
8
Views
1K
Replies
2
Views
2K
Top