Engineering Mathematics - Laplace Transforms

Let f(t) be a function of t defined for all positive values of t. The Laplace transform of f(t) denoted by L{f(t)} = ∫₀^∞ e^(-st)f(t)dt, provided that the integral exists where s is a parameter which may be a real or com...

The Dirac-delta function ($\delta(t - t_0)$) for $t, t_0 \in \mathbb{R}$, has the following property $\int_a^b \varphi(t)\delta(t - t_0)dt = \begin{cases} \varphi(t_0) & a 0$; $\mathcal{L}(\delta(t - a)) = F(s)$ is

$F(s)$ is the Laplace transform of the function $f(t) = 2t^2e^{-t}$. $F(1)$ is ________ (correct to two decimal places).