Question 1177657: Background info: In this task, you will practice finding the area under a nonlinear function by using rectangles. You will use graphing skills in addition to the knowledge gathered in this unit. Sketch the graph of the function y = 20x − x2, and approximate the area under the curve in the interval [0, 20] by dividing the area into the given numbers of rectangles.
Question: Use five rectangles to approximate the area under the curve.
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
The prescribed interval has length 20; approximating the area under the curve using 5 rectangles means the width of each rectangle is 4.
The heights of the 5 rectangles, if we use left sides, are f(0), f(4), f(8), f(12), and f(16). If we use the right sides of the rectangles for the heights, the heights are f(4), f(8), f(12), f(16), and f(20).
In this problem it doesn't make any difference in the answer, because f(0) and f(20) are equal.
You can do the actual calculations. The area is
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