Laplace Transform of t u(t-2) using Basic Definition

[tommyhakinen]

Homework Statement

find the laplace transform of g(t) = t u(t-2) using the basic definition.

Homework Equations

L{f(t)} = ∫f(t)e^-stdt from 0 to infinity

The Attempt at a Solution

I am able to get the transform by applying the t-shifting property. However, how do I do it by using basic definition? thanks.

 

[HallsofIvy]

Homework Statement

find the laplace transform of g(t) = t u(t-2) using the basic definition.

Homework Equations

L{f(t)} = ∫f(t)e^-stdt from 0 to infinity

The Attempt at a Solution

I am able to get the transform by applying the t-shifting property. However, how do I do it by using basic definition? thanks.

By integrating! Since H(x) is defined to be 0 for x< 0, 1 for x>= 0, H(t-2)= 0 for t< 2, 1 for t<= 2.
$$L{f(t)}= \int_2^\infty t e^{-st}dt$$
That should be easy.

 

[tommyhakinen]

Thank you very much. One more question. what is the inverse laplace transform of 1? Is it possible to get it? if there is, what can be done? thanks..