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Thread: expressing functions as other functions to solve laplace transforms

  1. #1
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    expressing functions as other functions to solve laplace transforms

    expressing functions as other functions to solve laplace transforms-20171018_154153.jpg
    I think I know the why...because it is expressed in the definition but I have no idea how to go about it. Is there a nice video or demonstration on how to accomplish these tasks?
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    Re: expressing functions as other functions to solve laplace transforms

    U(x- 4) is the "unit step function" that is 0 for x< 4, 1 for x\ge 4. The Laplace transform of that is \int_0^\infty e^{-st}u(s- 4)ds= \int_4^\infty e^{-st}ds. If you let x= s- 4, that becomes \int_0^\infty e^{-(x+ 4)t}dx= e^{-4t}\int_0^\infty e^{-xt}dx= e^{-4t}L(1).
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