Question

fun laplace question

Answer 1

given the piecewise function
f(t)= { t 0<= t< 1
{ 0 t>=1

the step unit function would look like

\[f(t)=t-t\mathcal{U}(t-1)\]

so would the laplace of that be the same as the laplace of the piecewise function?

(obvious answer would be yes assuming i didnt write the unit step function wrong, but i calculated the laplace using the piecewise function rather than a step function and a completely different answer than i was suppose to)

Answer 2

answer is yes
although calculating using the step function is much quicker if you know the laplace transform of unit functions than integrating the piece wise functions