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Math Help - Laplace Inverse

  1. #1
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    Laplace Inverse

    Laplace Inverse of 1 is 1/s or Deta(t) I am confused , can anybody give me confirm answer

    Thanks a lot in advance
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  2. #2
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    Re: Laplace Inverse

    Have you tried taking the Laplace transform of those?
    The Laplace transform of f(x) is, by definition, \int_0^\infty e^{-sx}f(x)dx
    So what are \int_0^\infty (1)e^{-sx} dx and \int_0^\infty (\delta(x))e^{-sx}dx?
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  3. #3
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    Re: Laplace Inverse

    I know that Laplace of 1 is 1/s but I am not getting what is Laplace Inverse of 1. Also I am not clear about answer given by you

    Thanks for the reply
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  4. #4
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    Re: Laplace Inverse

    Surely, you understand the relation between a "Laplace transform" and its inverse? (Or, for that matter, any kind of operation and it inverse!)

    Yes, L(1)= \int_0^\infty e^{-st}(1)dt= \left[-\frac{1}{s}e^{-st}\right]_0^\infty= \frac{1}{s} so 1 is the "inverse Laplace transform" of \frac{1}{s}, not 1.

    The Laplace transform of [tex]\delta(x)[\tex] is L(\delta(x))= \int_0^\infty e^{-st}\delta(t)dt= e^0= 1.

    Okat, NOW what is the inverse Laplace transform of "1"?
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  5. #5
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    Re: Laplace Inverse

    According to me its Delta function
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