HELP ME IN THIS PROBLEMS

Use Definition 7.1.1. Definition 7.1.1 Laplace Transform f(t ) = 10, cos(t), Ost 0)Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral If(t)} = e -stf(t) dt O is said to be the Laplace transform of f, provided that the integral converges. to find / {f(t)). (Write your answer as a function of s.) f(t) = the-8t Rf(t)} (5 > -8)Use Definition 7.1.1. Definition 7.1.1 Laplace Transform fit ) 1 1 Complete the integral(s) that defines {{f(t)}. LXf(t)) = dt + t Find {{f(t)}. (Write your answer as a function of s.) (5 > 0)Find /{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) f(t) = sin(6t + 4) S {{f(t)} = S 2 a XConsider the following initial-value problem. 2y" + 28y' + 99y = 0, y(0) = 2, y'(0) = 0 Take the Laplace transform of the differential equation and solve for /{y). (Write your answer as a function of s.) Ly} = Use the Laplace transform to solve the given initial-value problem. y(t) =