# If integral equal to zero, then?

1. Mar 6, 2013

### kennethkhoo

1. The problem statement, all variables and given/known data
if this statement is true:
$\int_0^\infty f(x) dx= 0$
then is this true?
$f(x) = 0$ in domain $x\in [0,\infty)$

2. Relevant equations
-NA-

3. 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...

2. Mar 6, 2013

### SteamKing

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

3. Mar 6, 2013

### ehild

Its improper integral is not defined.

ehild

4. Mar 6, 2013

### kennethkhoo

-deleted: multiple post-

5. Mar 6, 2013

### kennethkhoo

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

6. Mar 6, 2013

### ehild

That will do ...

ehild