The Laplace Transform of a continuous function f(t) is given by F(s) = ??? f(t)e??? dt Find the Laplace Transform of the following functions: (a) f(t) = 1 (b) f(t) = t (c) f(t) = sin(t)
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Given: \[ F(s) = \int_{0}^{\infty} f(t)e^{-st} dt \] Substitute f(t) = 1: \[ F(s) = \int_{0}^{\infty} 1 \cdot e^{-st} dt \] \[ F(s) = \int_{0}^{\infty} e^{-st} dt \] \[ F(s) = \left[ \frac{e^{-st}}{-s} \right]_{0}^{\infty} \] \[ F(s) = \frac{1}{s} \] ** Show more…
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