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Math Help - Laplace Transform

  1. #1
    Super Member craig's Avatar
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    Laplace Transform

    Just started a course on Laplace Transforms and I just want to check that I'm going about things in the right way.

    Find the Laplace transform X(s) of x(t) = (1-e^{-3t}) h(t).

    So, firstly we get:

    X(s) = \int_0^{\infty} (1-e^{-3t}) e^{-st} dt

    = \int_0^{\infty} e^{-st} - e^{-(3+s)t}  dt

    = \left[ \frac{-e^{-st}}{s} + \frac{e^{-(3+s)t}}{3+s} \right]_0^{\infty}

    = \left( 0 + 0 \right) - \left( \frac{-1}{s} + \frac{1}{3+s} \right)

    = \frac{3}{s(s+3)}

    Does the above seem about right?
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  2. #2
    A Plied Mathematician
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    Re: Laplace Transform

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  3. #3
    Super Member craig's Avatar
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    Re: Laplace Transform

    You have actually just made my day with that WolframAlpha link! Cheers for the reply.
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  4. #4
    A Plied Mathematician
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    Re: Laplace Transform

    Yeah, something about preferring to teach people to fish instead of handing them a fish. Now you can check all your own LT computations.
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  5. #5
    Super Member craig's Avatar
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    Re: Laplace Transform

    You make a valid point my friend.
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