How do I take the laplace of this?

[shreddinglicks]

Homework Statement

Find F(S)

Homework Equations

L[e^(2-t)U(t-2)]

The Attempt at a Solution

a = 2

and using the laplace table I got:

e^(-2s)/(s-2)

answer should be:

e^(-2s)/(s+1)

 

[Mark44]

Homework Statement

Find F(S)

Homework Equations

L[e^(2-t)U(t-2)]

The Attempt at a Solution

a = 2

and using the laplace table I got:

e^(-2s)/(s-2)

answer should be:

e^(-2s)/(s+1)

$e^{2 - t} = e^2 \cdot e^{-t}$
$\mathcal{L}[e^{at}] = \frac{1}{s - a}$

Plus, you need to deal with that u(t - 2).

 

[Orodruin]

I would not split $e^{2-t}$, the 2 is useful for using with the Heaviside function to just make the translation, giving the $e^{2s}$ factor of the result.

 

[Mark44]

Good point.

 

[vela]

Homework Statement

Find F(S)

Homework Equations

L[e^(2-t)U(t-2)]

The Attempt at a Solution

a = 2

What is $a$ supposed to represent?

and using the laplace table I got:

e^(-2s)/(s-2)

What was your thinking in coming up with this?

 

[Dustinsfl]

Why not work from the definition:
\begin{align}
\int_0^{\infty}e^{2-t}\mathcal{U}(t-2)e^{-st}dt &= e^2\int_2^{\infty}\exp[-t(1 + s)]dt\\
&= \ldots
\end{align}