Consider the following waveform. [ f(t)=150left(e^{-1000 t} ight) sin (2000 t) u(t) ] (a) Using Laplace, take

Consider the following waveform.

\[
f(t)=150\left(e^{-1000 t}\right) \sin (2000 t) u(t)
\]

(a) Using Laplace, take the time derivative of the waveform.

(b) Integrate the result found in part (a) and see if you recover the original function. Explain any discrepancy.