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<2\\t^2-4t+8&\text{for }t\ge2\end{cases}`


`\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=(2e^(-2s))/(s^3)+\frac{4e^(-2s)}s`