If integral equal to zero, then?

[kennethkhoo]

Homework Statement

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

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 $\infty/2$, except it doesn't exist.

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

 

[SteamKing]

What if f(x) = sin(x)?

 

[ehild]

What if f(x) = sin(x)?

Its improper integral is not defined.

ehild

 

[kennethkhoo]

-deleted: multiple post-

 

[kennethkhoo]

actually I think it might be er..
$f(x)=sin(x)$ for $x=[0,2\pi]$
$f(x)=0$ for others

 

[ehild]

That will do ...

ehild