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
Hey frankitm.
Hint: Look at the Heaviside function:
Heaviside step function - Wikipedia, the free encyclopedia
Indeed, your fuction can be written as
$\displaystyle g(t)=t\theta(t-3)$
where $\displaystyle \theta(x)$ is the Heaviside funcion. The Laplace transform of your function is
$\displaystyle \mathcal{L}[g](s)=\int_{0}^{\infty}g(t)e^{-st}dt=\int_{3}^{\infty}te^{-st}dt$
You can do that integral by parts.