Find the Laplace transform of the function f(t)={..

f(t)=
{ t, 0<= t < 1,
{ 1, t>= 1.


Appreciate the help !

You can write f in terms of the unit step function.

f(t) = t - tU(t - 1) + U(t - 1) = t - (t - 1)U(t - 1).

Then use the following shift theorem:

If L{g(t)} = G(s), then L{g(t - a)U(t - a)} = e^(-as)G(s).

So for your function

L{f(t)} = 1/s² - e^(-s)/s² = (1 - e^(-s))/s².

You can also use the definition and compute the appropriate integral. You'll arrive at the same result.