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Question 5.4.4: Determine the Laplace transform of f (t )=u(t −a)−u(t −b).

Determine the Laplace transform of f (t )=u(t −a)−u(t −b).

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Because we know L[u(t −a)] = e^{−as}/s, we can use the linearity of the Laplace transform to find

L[u(t −a)−u(t −b)] = \frac {1}{s} e^{−as} − \frac {1}{s} e^{−bs} = \frac {1}{s} (e^{−as} −e^{−bs} )

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