Prerequisites for Laplace Transforms

[MisterMan]

Hi, I was wondering what the prerequisites are for doing Laplace Transforms. I'm just a little confused with one of the examples :

$$\int_0^{\infty} = e^{-sx} dx = [e^{-sx}/s]_0^{\infty} = 1/s$$

I understand that $$e^{-s(0)}$$ is 1. But where does the $$e^{-s(\infty)}$$ part go? Is there something I should cover before this, in the book I have, the chapters before Laplace transforms that I haven't done are Double Integration, Triple Integration, Beta and Gamma Functions.

 

[n.karthick]

regarding your first doubt $e^{-s\infty} =e^{-\infty}$ because anything multiplied with infinity is again infinity and
$e^{-\infty}=0$

 

[MisterMan]

Oh my, I forgot I was dealing with a negative power! Of course:

$$e^{-\infty} = 1/e^{\infty} = 0$$

Just one of those mental blocks! Thanks n.karthick.

 

[hunt_mat]

You have to be careful about domains, make sure that you have a half infinite domain before you can apply it.

Mat