Question about laplace transform limits

[quietrain]

if say the function

f(t) is 0 from 1 to 2
is 1 from 2 to 3

if i laplace transform it , for f(t) = 1, i get f(s) = 1/s

so what are the limits for my s ? is it still 2 to 3?

thanks!

 

[HallsofIvy]

No, the Laplace transform of your function is NOT 1/s. That is the Laplace transform of f(x)= 1 for all x.

In order to have a Laplace transform, a function has to be defined for all non-negative number. It doesn't make any sense to talk about a function that is only defined between 1 and 3 as you have here.

Instead, let f(x)= 1 for x between 2 and 3 and 0 for all other non-negative x. Then the Laplace transform is
$$\int_0^\infty f(x)e^{-sx}dx= \int_2^3 e^{-sx}dx= \left[\frac{-1}{s}e^{-sx}\right]_2^3$$
$$= \frac{e^{-2s}- e^{-3s}}{s}$$
and s can have any value. The values of "s" have nothing to do with the values of "x".

 

[quietrain]

ah thank you very much