Laplace transform of step function

[ElijahRockers]

Homework Statement

Find laplace trasform of g(t)
g(t) = 0 for 0<t<1, t^2 for t>1

So this can be re-written as g(t) = t²*u₁(t), where u is the unit step function.

By using the fact that L(u_c(t)f(t-c)) = e^-csF(s) i am trying to take the laplace...

So in this case, f(t-c) = t² ... so then does f(t) = (t+1)²?

if so, I get L(f(t)) = e^-s*L(t²+2t+1) which I can evaluate to get

e^-s(2/s³ +2/s² +1/s)

but I'm not sure if that whole shifting function thing I did is correct, specifically, f(t)=(t+1)². the book's example uses a trig function that is already shifted so I am a little unsure of how to proceed

Thanks.

 

[vela]

Probably the easiest way to rewrite the function is to let u=t-1, so that t=u+1 and
$$ t^2 = (u+1)^2 = (t-1)^2 + 2(t-1) + 1$$ which is what you had. You could also check your answer by evaluating the integral
$$\int_1^\infty t^2 e^{-st}\,dt$$ and see if you get the same answer.