Could someone show me how to do the following Laplace transform?
f(t) =
e^(2t) if 0 < t < 8
1 if t > 8
F(s) = ?
I'm pretty lost. Thanks for any help.
Well we can do thus using just the definition of the Laplace Transform:
$\displaystyle
(\mathcal{L} f) (s) = \int_0^{\infty} f(t) e^{-st} dt
= \int_0^8 e^{2t}e^{-st} dt + \int_8^{\infty} e^{-st}dt
= \int_0^8 e^{t(2-s)} dt + \int_8^{\infty} e^{-st}dt
$
........ $\displaystyle =\frac{1}{s-2}[1-e^{8(2-s)}] + \frac{e^{-8s}}{s}$
RonL