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(e^{-t})=\\displaystyle\\int_{0}^{\\infin}e^{-st}e^{-t}dt"

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

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

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


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