Laplace transform

jwang34

1. The problem statement, all variables and given/known data
Given f(t)= 2 if 0<=t<1, and t if t>=1 I need to find the laplace transform.

2. Relevant equations
Using the second shifting theorem:
f(t)= 2(1-u(t-1))+t(u(t-1)), which is the heaviside function.

3. The attempt at a solution

The first term, I understand. It is 2-2u(t-1) which I got the transform to be:
(2/s)-(2/s)(e^-s). The second term I'm a little fuzzy. I think I need to shift the t, so I guess I would have (t-1)u(t-1). But I'm not sure if this is right. So any help is greatly appreciated.