For Problems 1–12, find the Laplace transform of the given function using the definition of the Laplace transform. 1. 5 2. t 3. e^{2t} 4. e^{-t} 5. sin 2t 6. cos 3t 7. 5 sinh 2t 8. e^{t} cos 2t 9. f(t)= {0 (0 ? t < 1); 1 (1 ? t)} 10. f(t)= {1 (0 ? t < 1); 0 (1 ? t)} 11. f(t)= {sin t (0 ? t < ?); 0 (t ? ?)} 12.
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For a given function f(t), its Laplace transform F(s) is defined as: $$ F(s) = \mathcal{L}\{f(t)\} = \int_0^{\infty} e^{-st} f(t) dt $$ Now, let's find the Laplace transforms for the given functions: Show more…
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