Express f (t) in terms of the Heavisides shifting function and find its Laplace transform: f(t) = {(t^2, 0 <= t < 2) (4t, 2 < =t < 4) (8, t >= 4)

Question

f(t) = {(t²,       0 <= t < 2)

          (4t,       2 < =t < 4) 

          (8,        t >= 4)}

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