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Homework Help: If integral equal to zero, then?

  1. Mar 6, 2013 #1
    1. The problem statement, all variables and given/known data
    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]

    2. Relevant equations

    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 [itex]\infty/2[/itex], except it doesn't exist.

    I would think it's false, but i need some example...
  2. jcsd
  3. Mar 6, 2013 #2


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    What if f(x) = sin(x)?
  4. Mar 6, 2013 #3


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    Its improper integral is not defined.

  5. Mar 6, 2013 #4
    -deleted: multiple post-
  6. Mar 6, 2013 #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
  7. Mar 6, 2013 #6


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    That will do ...

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