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Homework Help: Integrating exponent to get delta function

  1. Aug 9, 2014 #1
    Something i ran into while doing hw

    1. The problem statement, all variables and given/known data
    starting with
    [tex]\int{dx} e^{-ikx}\delta(x) = 1[/tex]
    we conclude by fourier theory that
    [tex]\int{dk} e^{+ikx} = \delta(x)[/tex]
    Now, i try to compute
    [tex]\int{dk} e^{-ikx}[/tex]

    (I've dropped the normalization factors of [tex]2\pi[/tex]. I beleive no harm is done by that)

    2. Relevant equations

    3. The attempt at a solution
    Method 1: change x to -x
    [tex]\int{dk} e^{-ikx} = \int{dk} e^{+ik(-x)} = \delta(-x) = \delta(x)[/tex]

    Method 2: change the integration parameter k to -k
    [tex]\int{dk} e^{-ikx} = -\int{dk} e^{+ikx} = -\delta(x)[/tex]

    So what did I do wrong here?

    thanks a lot
  2. jcsd
  3. Aug 9, 2014 #2
    I looked at it again. At my second method. I had to change the integral limits as well, and that fixes it.
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