Question

1) The Laplace transform of e^3t 2) The Laplace transform of sin(2t) 3) The Laplace transform of te^t 4) Let f(t) = 1 if 0 <= t <= 3, t - 2 if t > 3 5) The Laplace transform of e^t * t^3 + sin(3t)

Name: 1 the laplace transform of e3t 2 the laplace transform of sin2t 3 the laplace transform of tet 4 let ft 1 if 0t3 t 2 if t3 5 the laplace transform of ett3sin3t 24427
Uploaded: 2023-07-29T15:55:06-08:00
Duration: 1 min 29 s
Channel: Sri K
Description: 1 the laplace transform of e3t 2 the laplace transform of sin2t 3 the laplace transform of tet 4 let ft 1 if 0t3 t 2 if t3 5 the laplace transform of ett3sin3t 24427

          1) The Laplace transform of e^3t
2) The Laplace transform of sin(2t)
3) The Laplace transform of te^t
4) Let f(t) = 1 if 0 <= t <= 3, t - 2 if t > 3
5) The Laplace transform of e^t * t^3 + sin(3t)

Added by Brandon G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

07/29/2023

Step 1

1) The Laplace transform of $e^{3t}$ is given by: $$\mathcal{L}\{e^{3t}\} = \int_0^\infty e^{3t} e^{-st} dt = \int_0^\infty e^{-(s-3)t} dt$$ Using the formula for the integral of an exponential function, we get: $$\mathcal{L}\{e^{3t}\} = \frac{1}{s-3}$$ So, the Show more…

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1) The Laplace transform of e^3t 2) The Laplace transform of sin(2t) 3) The Laplace transform of te^t 4) Let f(t) = 1 if 0 <= t <= 3, t - 2 if t > 3 5) The Laplace transform of e^t * t^3 + sin(3t)