Consider the equation(t) + t0k(t )() d = f(t),in which f and k are known functions, and

Chapter 6, Problem 21

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Consider the equation(t) + t0k(t )() d = f(t),in which f and k are known functions, and is to be determined. Since the unknownfunction appears under an integral sign, the given equation is called an integral equation;in particular,it belongs to a class of integral equations known asVolterra integral equations.Take the Laplace transform of the given integral equation and obtain an expression forL{(t)} in terms of the transforms L{f(t)} and L{k(t)} of the given functions f and k. Theinverse transform of L{(t)} is the solution of the original integral equation.