# Math Help - Laplace Transformation

1. ## Laplace Transformation

1. $e^{-t}.u(t-1)$

My answer $\frac{s-1}{e^{s+1}}$
Book's answer $\frac{1}{s}$

How ? Can you please show it step by step ?

2. $cost.u(t-{pi})$

Can't start it all together.

2. Originally Posted by Altair
1. $e^{-t}.u(t-1)$

My answer $\frac{s-1}{e^{s+1}}$
Book's answer $\frac{1}{s}$

How ? Can you please show it step by step ?
I dont think it is $\frac1{s}$
Try to do it from definition:

$x(t) = e^{-t}.u(t-1)$
$X(s) = \int_{0}^{\infty} e^{-t} e^{-st}u(t-1) \, dt = \int_{1}^{\infty} e^{-(s+1)t}\, dt = -\frac{e^{-(s+1)t}}{s+1}\bigg{|}_{1}^{\infty} = \frac{e^{-s-1}}{s+1}$