Figure (a) shows a vacant lot with a 120-ft frontage L in a development. To esti

Question

Figure (a) shows a vacant lot with a 120-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, 120], we see that the problem is mathematically equivalent to that of finding the area under the graph of f on [0, 120]. To estimate the area of the lot using a Riemann sum, we divide the interval [0, 120] into four equal subintervals of length 30 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 = 15, 45, 75, and 105. What is the approximate area of the lot?

Explanation / Answer

The figure is not visible to me.

So, basically, we look at figure B and then find out the values of the function at x = 15 , 45 , 75 and 105.

I shall call these values as a,b,c and d

Now, simply add a+b+c+d first

And then to this, multiply the delta(x), which here is 30(length of the subintervals)

So, final answer is :

30(a + b + c + d) for the area

,.... where a,b,c,d are the values of the graph at exactly x = 15,45,75 and 105 respectively.

If this was unclear in any way, please comment and I can explain more in depth here

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