Finding the laplace transform of a wave?
The easiest way is to define \$f(t)\$ as a piecewise function

$$f(t)=\begin{cases}\frac{100}{0.002}\cdot t,&amp;0\le t\le 2\cdot 10^{-3}\\
100-\frac{100}{0.002}\cdot (t-2),&amp;2\cdot 10^{-3}&lt;t\le 4\cdot 10^{-3}\\
0,&amp;\text{otherwise}\end{cases}\tag{1}$$

Then with the definition of the Laplace transform

$$F(s)=\int_{-\infty}^{\infty}f(t)e^{-st}dt$$

you just split the integral and use the top expression in (1) in the interval \$[0,2]\$, and the bottom expression in the interval \$[2,4]\$.

Another way to solve such problems is to compute the Laplace transform of the derivative of \$f(t)\$, which is a piecewise constant function. The derivative of \$f(t)\$ can be written using the step function \$u(t)\$:

$$f'(t)=k\cdot[u(t)-2u(t-2)+u(t-4)]\tag{2}$$

where \$k=100/0.002\$, and where I've used units of milliseconds. From (2) you can immediately write down the result by noting that the Laplace transform of \$u(t-t_0)\$ is \$e^{-st_0}/s\$. As soon as you have the Laplace transform of \$f'(t)\$, you just need to divide by \$s\$ to obtain the Laplace transform of \$f(t)\$.

And, by the way, \$100/0.002=50000\$, and not \$5000\$.