Chapter 5.4, Problem 61E

Problems 61 and 62 refer to the following figure showing two parcels of land along a river:

61. You want to purchase both parcels of land shown in the figure and make a quick check on their combined area. There is no equation for the river frontage, so you use the average of the left and right sums of rectangles covering the area. The 1,000-foot baseline is divided into 10 equal parts. At the end of each subinterval a measurement is made from the baseline to the river, and the results are tabulated. Let x be the distance from the left end of the baseline and let h(x)

be the distance from the baseline to the river at x. Use L₁₀ to estimate the combined area of both parcels, and calculate an error bound for this estimate. How many subdivisions of the baseline would be required so that the error incurred in using L_n would not exceed 2,500 square feet?

x	0	100	200	300	400	500
h(x)	0	183	235	245	260	286

x	600	700	800	900	1,000
h(x)	322	388	453	489	500