# Derivation on Laplaican of integral of a function

• Nov 17th 2012, 05:52 AM
dolle39
Derivation on Laplaican of integral of a function
Hi everyone! Im trying to understand the Laplacian transofrmation of an integral but with no success. Can someone
please sohw me the derivation of the following equation:

$L{u(t))(s) = L(\int_0^{\inf} y(x)\,dx)(s) = Y(s)/s$

Best Regards
• Nov 17th 2012, 04:49 PM
chiro
Re: Derivation on Laplaican of integral of a function
Hey dolle39.

Consider using Fubini's Theorem and evaluating the double integral:

Fubini's theorem - Wikipedia, the free encyclopedia
• Nov 18th 2012, 02:54 AM
dolle39
Re: Derivation on Laplaican of integral of a function
Thanks for answer. I still don't really see it. Wouldn't that just be the laplacian of y(t) , i.e Y(s)? Where does 1/s come in?
• Nov 18th 2012, 06:04 PM
chiro
Re: Derivation on Laplaican of integral of a function
Did you try calculating the double integral corresponding to one integral being 0 to infinity for dx and 0 to infinity for s?