Consider the equation (t) + _ t 0 k(t ) () d = f (t), in which f and k are known

QUESTION:

Consider the equation (t) + _ t 0 k(t ) () d = f (t), in which f and k are known functions, and is to be determined. Since the unknown function appears under an integral sign, the given equation is called an integral equation; in particular, it belongs to a class of integral equations known as Volterra integral equations7. Take the Laplace transform of the given integral equation and obtain an expression for L{ (t)} in terms of the transforms L{ f (t)} and L{k(t)} of the given functions f and k. The inverse transform of L{ (t)} is the solution of the original integral equation. 1