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Delta Dirac function property

  1. Mar 12, 2013 #1
    Prove that.

    [itex]\int_a^b f(x)g' (x)\, dx = -f(0)[/itex]


    This is supposed to be a delta Dirac function property. But i can not prove it.
    I thought using integration by parts.

    [itex] \int_a^b f(x)g' (x)\, dx = f(x)g(x) - \int_a^b f(x)'g (x)\, dx [/itex]

    But what now?


    Some properties:


    [itex] \delta [g(x)] = \sum \frac{1}{|g'(xi)|} [/itex]

    [itex] \int_a^b f(x)\delta(x-xi)\, dx = [/itex]

    [itex]f(x_{0})[/itex] if [itex]a<x_{0}<b[/itex]
    0, other cases.




    I just need a tip please.
     
  2. jcsd
  3. Mar 12, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    In general, this is wrong. Are there any additional constraints on f,g,a,b?
    If that would be true, all integrals would be trivial ;).
     
  4. Mar 12, 2013 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What does this have to do with the "Dirac Delta Function"? Is g' supposed to be the Dirac Delta Function? What is g?
     
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