# Math Help - Laplace transformation and heaviside function

1. ## Laplace transformation and heaviside function

If H is the Heaviside function with

H(t-a)=0, t<a
H(t-a)=1, t>a

find the laplace transformation of H(t-a)g(t).

I know how to find the transformation of H(t-a)g(t-a), but I can't do this one.

2. Originally Posted by Ricko
If H is the Heaviside function with

H(t-a)=0, t<a
H(t-a)=1, t>a

find the laplace transformation of H(t-a)g(t).

I know how to find the transformation of H(t-a)g(t-a), but I can't do this one.
$
\mathfrak{L} \left[H(t-a)g(t)\right](s)=\int_0^{\infty} H(t-a)g(t)e^{-st}\;dt=\int_a^{\infty} g(t)e^{-st}\;dt=$
$e^{-as}\int_0^{\infty} g(u+a)e^{-su}\;du=e^{-as}\mathfrak{L} \left[g(x+a)\right](s)
$

CB