I want to show that if the integral offwith upper limitband lower limitaisequal to 0

thenf(x) = 0for allx in [a,b]?

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- Nov 14th 2006, 12:41 PMdopiintegral question
I want to show that if the integral of

**f**with upper limit**b**and lower limit**a**is**equal to 0**

then**f(x) = 0**for all**x in [a,b]?** - Nov 14th 2006, 01:06 PMPlato
That is not true. Here is a counter-example.

- Nov 14th 2006, 01:07 PMThePerfectHacker
Which is clearly not true,

the identity function on :eek:

Perhaps, you wish to show that if

And if,

Then,

But that is also not true.

Consider an analoge of the Dirac Delta Function.

That is, the function is discontinous at one point with a different value and elsewhere is equal to zero. - Nov 14th 2006, 01:13 PMSoroban
Hello, dopi!

Quote:

I want to show that if , then for all

You are saying:

. . If the area 'under a curve' on [a,b] is zero, the curve must be the*x-axis.*

This is not true . . .

Counter-examples: . .

- Nov 14th 2006, 01:14 PMdopi

**yea thats wat i wanted to show if f(x)>0 and if the integral of f= 0 with upper limit b and lower limit a then f(x)= 0 for all x in [a,b]...but i dont get what this has to do with the qiestion**"Consider an analoge of the Dirac Delta Function.

That is, the function is discontinous at one point with a different value and elsewhere is equal to zero" - Nov 14th 2006, 01:23 PMThePerfectHacker
Consider the function,

on and for

Then, the integral still exists,

though it is discontinous on this interval.

Yet,

for all the points in

Perhaps, you want to show and is continous on the interval. (Look how many conditions you have to fullfil to demonstrate what you have said!) - Nov 14th 2006, 01:26 PMdopi