Answer to Question #343122 in Differential Equations for Tobias Felix

Question #343122

Find the Laplace transforms of the following function:

5. L{t^4}


1
Expert's answer
2022-05-23T23:53:11-0400
"{\\cal L}\\{f\\}(s)=\\int_0^{\\infty}f(t)e^{-st}dt"

"{\\cal L}\\{t^4\\}(s)=\\int_0^{\\infty}t^4e^{-st}dt"

"=\\frac{d^4}{ds^4}\\int_0^{\\infty}e^{-st}dt=\\frac{d^4}{ds^4}(1\/s)=\\frac{24}{s^5}"


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