i have signal as shown on the attached image, and i need to introduce it analytically and apply Laplace transformation on it...

signal is :

and i have done this

$\displaystyle \displaystyle f(t) = 10\cdot t \cdot u(t) - 20 \cdot (t-10) \cdot u(t-10) +10\cdot (t-20) \cdot u(t-20) $

that's as far as writting it analytically... (is this correct ? )

now with LT ...

$\displaystyle \displaystyle F(S)= 10 S \frac {1}{S} -20e^{-10S} \frac {1}{S} + 10 e^{-20S} \frac {1}{S} = $

$\displaystyle =10 - 20 e^{-10S}\frac {1}{S} + 10 e^{-20S}\frac {1}{S} $

P.S. sorry for bad image