# Math Help - laplace transform..

1. ## laplace transform..

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$\mathcal{L}^{-1}\left\{e^{-as}F\left(s\right)\right\}=u\left(t-a\right)f\left(t-a\right)
$

i have
$
\frac{2e^{-s}}{s}
$

i know that 1/s is 1
but i cant do a shift of t by 1 here
there is not t in the end
??

2. Originally Posted by transgalactic
[font=monospace]

$\mathcal{L}^{-1}\left\{e^{-as}F\left(s\right)\right\}=u\left(t-a\right)f\left(t-a\right)
$

i have
$
\frac{2e^{-s}}{s}
$

i know that 1/s is 1
but i cant do a shift of t by 1 here
there is not t in the end
??
$
2u(t-1)
$

CB

3. Originally Posted by transgalactic
[font=monospace]

$\mathcal{L}^{-1}\left\{e^{-as}F\left(s\right)\right\}=u\left(t-a\right)f\left(t-a\right)
$

i have
$
\frac{2e^{-s}}{s}
$

i know that 1/s is 1
but i cant do a shift of t by 1 here
there is not t in the end
??
If f(t) = 1 then f(t - 1) = 1.

Alternatively, you can use the well known result that $\mathcal{L}^{-1} \left[ \frac{F(s)}{s}\right] = \int_0^t f(u) \, du$ where $f(t) = \mathcal{L}^{-1} [F(s)]$. Note that $\mathcal{L}^{-1} [e^{-s}] = \delta (t - 1)$ (the Dirac delta-function).