Using a table of Laplace transforms, find the Laplace transform of $f(t)=t e^{-3 t}$.
A) $\frac{1}{(s-3)^{2}}$
B) $\frac{\mathrm{s}}{(\mathrm{s}+3)^{2}}$
C) $\frac{s^{2}}{s-3}$
D) $\frac{1}{(s+3)^{2}}$

Question

Quizplus · Accepted Answer

The Laplace transform of $t e^{-at}$ is $\frac{1}{(s+a)^2}$. Here, $a = 3$, so the transform is $\frac{1}{(s+3)^2}$.

Using a Table of Laplace Transforms, Find the Laplace Transform f(t)=te−3tf(t)=t e^{-3 t}f(t)=te−3t

Using a Table of Laplace Transforms, Find the Laplace Transform $f(t)=t e^{-3 t}$