# How do I take the laplace of this?

1. Dec 4, 2014

### shreddinglicks

1. The problem statement, all variables and given/known data
Find F(S)

2. Relevant equations
L[e^(2-t)U(t-2)]

3. 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)

2. Dec 5, 2014

### Staff: Mentor

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

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

3. Dec 5, 2014

### Orodruin

Staff Emeritus
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.

4. Dec 5, 2014

Good point.

5. Dec 5, 2014

### vela

Staff Emeritus
What is $a$ supposed to represent?

What was your thinking in coming up with this?

6. Dec 6, 2014

### 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}

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