Answer to Question #343128 in Differential Equations for Tobias Felix

Question #343128

Find the Laplace transforms of the following function:

10. L{e^-t}


1
Expert's answer
2022-05-24T08:27:04-0400
F(s)=L(et)=0estetdtF(s)=L(e^{-t})=\displaystyle\int_{0}^{\infin}e^{-st}e^{-t}dt

=limA0Ae(s+1)tdt=[e(s+1)ts+1]A0=\lim\limits_{A\to\infin}\displaystyle\int_{0}^{A}e^{-(s+1)t}dt=[-\dfrac{e^{-(s+1)t}}{s+1}]\begin{matrix} A \\ 0 \end{matrix}

=0+1s+1=1s+1=-0+\dfrac{1}{s+1}=\dfrac{1}{s+1}

L(et)=1s+1L(e^{-t})=\dfrac{1}{s+1}


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