Figure (a) shows a vacant lot with a 100-ft frontage L in a development. To esti

Question

Figure (a) shows a vacant lot with a 100-ft frontage L in a development. To estimate its area, we introduce a coordinate system so that the x-axis coincides with the edge of the straight road forming the lower boundary of the property, as shown in Figure (b). Then, thinking of the upper boundary of the property as the graph of a continuous function f over the interval [0, 100], we see that the problem is mathematically equivalent to that of finding the area under the graph of f on [0, 100]. To estimate the area of the lot using Riemann sum, we divide the interval [0, 100] into five equal subintervals of length 20 ft. Then, using surveyor's equipment, we measure the distance from the midpoint of each of these subintervals to the upper boundary of the property. These measurements give the values of f(x) at x = 10, 30, 50, 70, and 90. What is the approximate area of the lot?

Explanation / Answer

Figure (a) not given

divide the interval [0, 100] into five equal subintervals of length 20 ft , so x =(100-0)/5=20

by midpoint

approximate area of the lot = x*[f(10)+f(30)+f(50)+f(70)+f(90)]

approximate area of the lot = 20*[f(10)+f(30)+f(50)+f(70)+f(90)]

in the above equation ,from the figure you have,just plug in the widths of lot at points x=10,30,50,70,90. then calculate ,to get answer with units as squarefeet

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.