# Math Help - Inverse Laplace transform

1. ## Inverse Laplace transform

can anyone tell me the inverse laplace transform of a constant???
Asap... urgently required....

2. Originally Posted by 000
can anyone tell me the inverse laplace transform of a constant???
Asap... urgently required....
$LT^{-1}[1] = \delta (t)$ where $\delta (t)$ is the Dirac delta function.

3. can u tell me how that happened???

4. Originally Posted by 000
can u tell me how that happened???
Because:

$(\mathcal{L}\ \delta)(s)=\int_0^{\infty} \delta(t)e^{-st}\ dt=\left. e^{-st}\right|_{t=0}=1$

(works better with the two-sided transform though)

RonL