Originally Posted by

**Diamondlance** I'm looking at my old Differential Equations textbook and struggling with a sticky point regarding Laplace transforms.

He defines the Laplace transform in the standard way, saying that the Laplace transform is valid for all s such that the integral converges.

In looking at one of the exercises, he asks for the Laplace transform of the piecewise function $\displaystyle f(t)=2t+1$ for $\displaystyle 0\le t<1$ and 0 for $\displaystyle t>1$. I obtained the correct answer $\displaystyle \displaystyle\frac{1-3e^{-s}}{s}+\displaystyle\frac{2-2e^{-s}}{s^2}$, but the author says in his solutions manual that this is valid for s>0. Why not for s<0 in this case? Since the integral involved is not improper there should be no issue...am I missing something obvious?