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A simple method of calculating Stieltjes integrals is proposed. The method is essentially the two-point (trapezoidal) rule from numerical analysis. Two theorems yielding error bounds are given. When error requirements are modest (two or three significant decimal places) the method is fast and inexpensive. Examples are given solving the Renewal equation from reliability theory. A program for an HP-41C hand calculator is given, which solves the renewal equation.
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