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

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- Apr 4th 2013, 08:25 PMfrankitmlaplace
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 - Apr 4th 2013, 09:21 PMchiroRe: laplace
Hey frankitm.

Hint: Look at the Heaviside function:

Heaviside step function - Wikipedia, the free encyclopedia - Apr 5th 2013, 03:51 AMRuunRe: laplace
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.