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.

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- May 25th 2007, 01:48 PMPvtBillPilgrimLaplace transform
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. - May 25th 2007, 02:07 PMCaptainBlack
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 - May 25th 2007, 02:25 PMPvtBillPilgrim
Makes sense.

Thank you very much.