# Thread: expressing functions as other functions to solve laplace transforms

1. ## expressing functions as other functions to solve laplace transforms

I think I know the why...because it is expressed in the definition but I have no idea how to go about it. Is there a nice video or demonstration on how to accomplish these tasks?

2. ## Re: expressing functions as other functions to solve laplace transforms

U(x- 4) is the "unit step function" that is 0 for x< 4, 1 for $x\ge 4$. The Laplace transform of that is $\int_0^\infty e^{-st}u(s- 4)ds= \int_4^\infty e^{-st}ds$. If you let x= s- 4, that becomes $\int_0^\infty e^{-(x+ 4)t}dx= e^{-4t}\int_0^\infty e^{-xt}dx= e^{-4t}L(1).$