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<br />) <br /> <br />~) <br /> <br />) <br /> <br />Values in column (9) are then added cumulatively, starting from zero, to <br /> <br /> <br />give the summation of the EAD of $42,645 shown in column (10). <br /> <br /> <br />Conceptual Framework for Computation: Ideally, the area under a <br /> <br /> <br />continuous curve with a known function, yk-f(x), can be determined by <br /> <br /> <br />integrating over the limits of the intervals of that function. The <br /> <br />concept of integration is based on breaking down the area under the curve <br /> <br />into rectangles, computing the areas of these rectangles, and summing the <br /> <br />results. The smaller the width of the rectangles (or the greater the <br /> <br />number of rectangles), the closer this summation is to the actual area. A <br /> <br />logical consequence of this is that if the number of rectangles approaches <br /> <br /> <br />infinity, the area under the curve is essentially defined. This, then, is <br /> <br /> <br />the basis for integration, and the justification for the procedure used by <br /> <br /> <br />the Corps to compute EAD. The concept can be grasped more readily by <br />examining Figure V-9. Damage-frequency points, taken from the simplified <br />sample estimates shown in Table V-3, are used to construct the curve shown <br /> <br />on this chart. The heights of the rectangles represent the average <br /> <br />damages shown in column 4. For example, the heights of the first and last <br /> <br />rectangles are 600,000 and 3,225,000, respectively. The widths of the <br /> <br />rectangles are the frequency intervals shown in column 2. Consequently, <br /> <br />the summation of the areas of all rectangles, i.e., the summation of all <br /> <br /> <br />the heights times the bases, yields the same result as in the sample <br /> <br /> <br />computation. However, it is well to remember that since the number of <br /> <br /> <br />rectangles is limited, the estimate derived is only an approximation of <br />the area under the curve. Estimates can be distorted, based on the number <br /> <br />of input points, and on the shape of the curve, except where the damage- <br /> <br />frequency curve is a straight-line. The straight-line damage-frequency <br /> <br />V-53 <br />