Mathematics, 26.03.2020 21:49 bravooyessenia
DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = [infinity] e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. Find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = t cos t ℒ{f(t)} = (s > 0)
Answers: 2
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![=\textit{Real part of} \{\Big[t\frac{e^{(-s+i)t}}{-s+i}\Big]_{0}^{\infty}-\int_{0}^{\infty}\frac{e^{(-s+i)t}}{-s+i}dt\}](/tpl/images/0565/8635/3ce8c.png)
![=\textit{Real part of} \{-\frac{1}{-s+i}\Big[\frac{e^{(-s+i)t}}{-s+i}\Big]_{0}^{\infty}\}](/tpl/images/0565/8635/ec35a.png)
![=\textit{Real part of}\Big[\frac{1}{(-s+i)^2}\Big]](/tpl/images/0565/8635/e1a8d.png)
![=\textit{Real part of}\Big[\frac{s^2+2i+1}{(s^2+1)^2}\Big]](/tpl/images/0565/8635/7fb95.png)
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DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)}...
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