The Laplace Transform turns a given function f = f(t) into a new function F = F(s) by way of an improper integral: F(3) = [we't dt. 0 Suppose f(t) = 2t + 12. (a) Find the set of real numbers 3 for which the improper integral defining F(3) converges. Answer in interval notation. (To enter 00, type \"inf\"; for 00, type \"-inf".) Answer: (b) Find a simple formula for F(3), valid on the interval described in part (a). 3 Answer: F(s) =