Answer to Question #127154 in Differential Equations for jse

Question

Find the Laplace transform of the given function.

f(t)={1, 0 ≤ t < 7
{ 0,t ≥ 7


Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).

L{f(t)}= _____________

Answer 1

$L \{ f(t) \} = \int\limits_{0}^{7} 1 \cdot e^{-st} dt + \int\limits_{7}^{\infty} 0 \cdot e^{-st} dt = -\cfrac{1}{s} \cdot \Big( e^{-st} \text{\textbar}_{0}^{7} \Big) = -\cfrac{1}{s} \Big( e^{-7t} - e^{0} \Big) = \cfrac{1 - e^{-7t}}{s}$