Consider the equation ?(t) + ? t 0 k(t ? ?)?(?) d? = f(t

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 equations. Take the Laplace transform of the given integral equation and obtain an expression for ?{?(t)} in terms of the transforms ?{f(t)} and ?{k(t)} of the given functionsf and k. The inverse transform of ?{?(t)} is the solution of the original integral equation.