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:

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

Best Regards

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

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?

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?