# Math Help - laplace

1. ## laplace

Hi guys, could you help me solve this simple problem, what happens is that I have a little doubt with the defining intervals of the function, thanks

Find the
Laplace transform of the given function

g(t)
= 0 t < 3
= t t
≥ 3

2. ## Re: laplace

Hey frankitm.

Hint: Look at the Heaviside function:

Heaviside step function - Wikipedia, the free encyclopedia

3. ## Re: laplace

Indeed, your fuction can be written as

$g(t)=t\theta(t-3)$

where $\theta(x)$ is the Heaviside funcion. The Laplace transform of your function is

$\mathcal{L}[g](s)=\int_{0}^{\infty}g(t)e^{-st}dt=\int_{3}^{\infty}te^{-st}dt$

You can do that integral by parts.