# f(t)=t^2,t >=1 f(t)=0,0<t<1 what is the laplace transform of f(t)

Laplace Transform of ${t}^{2}$ , for$t\ge 1$
$f\left(t\right)={t}^{2},t>=1$
what is the laplace transform of f(t)?
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Miah Scott
$f\left(t\right)={t}^{2}H\left(t-1\right)=\left[\left(t-1{\right)}^{2}+2\left(t-1\right)+1\right]H\left(t-1\right)$
$\mathcal{L}\left\{f\left(t\right)\right\}=\mathcal{L}\left\{\left[\left(t-1{\right)}^{2}+2\left(t-1\right)+1\right]H\left(t-1\right)\right\}={\mathrm{e}}^{-s}\left[\frac{2}{{s}^{3}}+2\cdot \frac{1}{{s}^{2}}+\frac{1}{s}\right]$