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
L{f}(s)=0f(t)estdt{\cal L}\{f\}(s)=\int_0^{\infty}f(t)e^{-st}dt

L{t4}(s)=0t4estdt{\cal L}\{t^4\}(s)=\int_0^{\infty}t^4e^{-st}dt

=d4ds40estdt=d4ds4(1/s)=24s5=\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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