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Math Help - integration of dirac delta times exponential

  1. #1
    Newbie omeganeu's Avatar
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    integration of dirac delta times exponential

    I have some confusion with this integral
    exp(-k(2t-t-t))(t-t)dt= exp(-2k(t-t))

    where exp(...) is the exponential function, the integration from 0 to t, k is a constant (and also t), (t-t) is Dirac delta function which equals 1 when t=t and zero when t≠t

    can any one explain to me how this was done?
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  2. #2
    Newbie omeganeu's Avatar
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    I notice that in this integration what happened only the variable t
    changed to t in the exponential function, is it a rule or something in this type of integration?
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  3. #3
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    Quote Originally Posted by omeganeu View Post
    I notice that in this integration what happened only the variable t
    changed to t in the exponential function, is it a rule or something in this type of integration?
    The sifting property of the Dirac Delta function has been used: \int_{- \infty}^{+\infty} \! f(x) \, \delta (x - x') \, dx = f(x').
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  4. #4
    Newbie omeganeu's Avatar
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    Thank you
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