Question

Find the laplace transform of the given function. (express your answer in terms of s. assume that s > 0.) f(t) = 0, t < 2 t2 − 4t + 8, t ≥ 2

Answer 1

$f(t)=\begin{cases}0&\text{for }t$

$\mathcal L_s\{f(t)\}=\displaystyle\int_0^\infty f(t)e^{-st}\,\mathrm dt$
$=\displaystyle\int_2^\infty(t^2-4t+8)e^{-st}\,\mathrm dt=\frac{2e^{-2s}}{s^3}+\frac{4e^{-2s}}s$