Laplace Transforms of Discontinuous functions

[Gilligan08]

Homework Statement

(t − 1)^2u(t − 1) Find the Laplace transform.

Homework Equations

L{f(t-a)u(t-a)}(s) = e^-as F(s)

The Attempt at a Solution

The solution manual says take f(t) = t^2, I don't see why? Why is f(t) not (t-1)^2?

 

[Dick]

Because t-1 is in the argument of f. If f(t-1)=(t-1)^2, I would say f(t)=t^2.