1) (I pt) a. Set up an integral for finding the Laplace transform of the following function: f(t) = 0 t + 3, 6 t where A b. Find the antiderivative (with constant term 0) corresponding to the previous part. c. Evaluate appropriate limits to compute the Laplace transform of f(t): F(s) = CU)(s)- d. Where does the Laplace transform you found exist? In other words, what is the domain of F(sh 2) (1 pt) From a table of imegrals, we know tat for a, bã¡ cos(M) dtcosbsin(he) a. Assume w is a constant, and use this antiderivative to compute the following improper integral: cos(wt)e-sat jun its 0 - or cos(ut)e-* dtim b. For which values of s do the limits above exist? In other words, what is the domain of the Laplace transform of cos(t) Evaluate the existing limit to compute the Laplace transform of cos u on the domain you determined in the previous at: F(s)-cos( wt)(s)-