Laplace transform of t*u(t-1)

[xemnas1]

Homework Statement

Find the laplace transform of;

t*u(t-1)

I always thought that the laplace transform of the function was;

(1/s^2) * (e^-s)

However, recently I was told that I was wrong!

I was told that I was wrong, because t*u(t-1) is not a function of (t-1). That in order to take the proper laplace transform of it, I needed it to turn it into a function of (t-1).

How can I do that? Can anyone help me find the proper laplace transform of my function, please?

 

[neo86]

okay, this isn't too hard, let's start out with the definition of the laplace transform:

$$\int_0^\infty t u(t-1) e^{-st} dt= \int_1^\infty t e^{-st} dt$$

and then you just need to evaluate the integral, which will give you something like:
$$\frac{e^{-s}(s+1)}{s^2}$$

 

[xemnas1]

Thank you, I did everything and got the same result. :]