 # Determine the Laplace transform of f(t)={(t,text( if ) 0<t<2),(8-3t, text( if ) 2 <=t<3),(t-4,text( if ) 3 <=t<=4),(0, text( if ) 4<t):} driliwra7 2022-09-12 Answered
Determine the Laplace transform of
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Hint: If
$f\left(t\right)=\left\{\begin{array}{cl}{f}_{1}\left(t\right)& 0⩽t<{c}_{1},\\ {f}_{2}\left(t\right)& {c}_{1}⩽t<{c}_{2},\\ {f}_{3}\left(t\right)& {c}_{2}⩽t<{c}_{3},\\ ⋮\\ {f}_{n-1}\left(t\right)& {c}_{n-2}⩽t<{c}_{n-1},\\ {f}_{n}\left(t\right)& t⩾{c}_{n-1}.\end{array}$
then
$f={f}_{1}+{u}_{{c}_{1}}\left({f}_{2}-{f}_{1}\right)+{u}_{{c}_{2}}\left({f}_{3}-{f}_{2}\right)+\cdots +{u}_{{c}_{n-1}}\left({f}_{n}-{f}_{n-1}\right)$
where ${u}_{c}\left(t\right)$ is step function.