SOLVED: Laplace Transform: Give a piecewise function2, 0 < t < 1 f(t) = 3t, 1 < t < 4 (0 < t < 4).Find F(s) using the definition of Laplace Transform:Answer: F(s) = ∫[0 to 1] 3te^(-st) dt ∫[1 to 4] 0 dt = 3/s^2 0 = 3/s^2Linear Property of Laplace Transform: Find the Laplace transform of the function given; f(t) = 2t'e^tAnswer: F(s) = ∫[0 to ∞] 2t'e^(-st) dt = -2/s^2First shift Property of Laplace Transform: Find the Laplace transform of the function given, f(t) = e^(-3t)sin(t)Answer: