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The bilateral Laplace transform of a function $f(t) = \begin{cases} 1 & \text{if } a \leq t \leq b \\  0 & \text{otherwise} \end{cases}$ is

  1. $\dfrac{a-b}{s} \\$
  2. $\dfrac{e^{s}(a-b)}{s} \\$
  3. $\dfrac{e^{-as}-e^{-bs}}{s} \\$
  4. $\dfrac{e^{s(a-b)}}{s}$
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