Problem 1: Use the definition of Laplace transform to transform the following functions; where It, a, B, y. are constants. Show your solution process and do not use a Laplace Transform table. (2 point each, 10 points total) F(s) = I{f(1))=], f(1)exp(-st)dt, s > 0 a. f (1) = 21 b. f (1) = (5t+2). c. f (1) = exp(-at). d. f(1) = sin(Bt), e. f (t) = sinh(yt)