# The Laplace transform of the signal u(t) – u(t-2) is ______________

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The Laplace transform of the signal u(t) – u(t-2) is ______________

(a) $\frac{e^{-2s}-1}{s}$

(b) $\frac{-e^{-2s}+1}{s}$

(c) $\frac{2}{s}$

(d) $\frac{-2}{s}$

The question was asked in a national level competition.

I would like to ask this question from Common Laplace Transforms topic in division Laplace Transform and System Design of Signals and Systems

by (42.1k points)
The correct answer is (b) $\frac{-e^{-2s}+1}{s}$

Easy explanation: X(s) = $\int_0^∞ x(t) e^{-st} \,dt$

Here, the given signal is u (t).

Hence, u (t) = 1 for all t>0 and = 0 for all t<0.

Again, the given signal is u (t-2).

Hence, u (t-2) = 1 for all t>2 and = 0 for all t<2.

So, limit is from 0 to 2

∴ Laplace of signal= $\int_0^2 e^{-st} \,dt$

= $\frac{-e^{-2s}+1}{s}$.

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