Question

use a definiçao da transformada de laplace para calcular L{(t)}

f(t)=3

Answer 1

Resolução da questão, veja:

Pela definição de transformada de Laplace, temos:

$\mathsf{\displaystyle F(s)=\mathcal {L}}\{f\}(s)=\displaystyle\int _{0}^{\infty }e^{-st}f(t)\,dt.}\\\\\\\\\ \mathsf{F(s)=\displaystyle\int_{0}^{\infty}e^{-st}~3~dt}}}}}}}~=>~\mathsf{\dfrac{e^{-st}}{-s}\bigg|_{0}^{\infty}}}}}}}\\\\\\\\\ \mathsf{\displaystyle\lim_{T~\to~\infty}\dfrac{e^{-sT}}{-s}}}-\mathsf{\dfrac{e^{-s0}}{-s}}}}\\\\\\\\\ \mathsf{0-\dfrac{e^{-s0}}{-s}}}}\\\\\\\\\ \large\boxed{\boxed{\boxed{\boxed{\mathsf{\mathcal {L}}\{f\}(s)=\dfrac{3}{s}}}}}}}}}}}}}}}}}}}}}}}}$

Ou seja, a transformada de Laplace da função f(t) = 3 é igual a f(s) = 3/s.

Espero que te ajude. '-'