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Math Help - Derivation on Laplaican of integral of a function

  1. #1
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    Derivation on Laplaican of integral of a function

    Hi everyone! Im trying to understand the Laplacian transofrmation of an integral but with no success. Can someone
    please sohw me the derivation of the following equation:

     L{u(t))(s) = L(\int_0^{\inf} y(x)\,dx)(s) = Y(s)/s

    Best Regards
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  2. #2
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    Re: Derivation on Laplaican of integral of a function

    Hey dolle39.

    Consider using Fubini's Theorem and evaluating the double integral:

    Fubini's theorem - Wikipedia, the free encyclopedia
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  3. #3
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    Re: Derivation on Laplaican of integral of a function

    Thanks for answer. I still don't really see it. Wouldn't that just be the laplacian of y(t) , i.e Y(s)? Where does 1/s come in?
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  4. #4
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    Re: Derivation on Laplaican of integral of a function

    Did you try calculating the double integral corresponding to one integral being 0 to infinity for dx and 0 to infinity for s?
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