If integral equal to zero, then?

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    Integral Zero
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Homework Help Overview

The discussion revolves around the implications of the integral of a function being equal to zero, specifically examining whether this necessitates that the function itself is zero over the specified domain. The subject area pertains to calculus and the properties of integrals.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the validity of the statement regarding the integral being zero and question whether there are functions that could satisfy this condition without being identically zero. Some suggest considering specific functions like sine to test the hypothesis.

Discussion Status

The discussion is ongoing, with participants offering examples and questioning the definitions and properties of functions in relation to their integrals. There is no explicit consensus yet, but some productive lines of inquiry have been initiated.

Contextual Notes

Participants are considering the behavior of functions over specific intervals and the implications of improper integrals, noting that certain functions may not have defined integrals over the entire range.

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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...
 
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What if f(x) = sin(x)?
 
SteamKing said:
What if f(x) = sin(x)?

Its improper integral is not defined.

ehild
 
-deleted: multiple post-
 
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
 
That will do ...

ehild
 

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