HELPP 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. Part A
Use five rectangles to approximate the area under the curve.
Part B
Use 10 rectangles to approximate the area under the curve.
Part C
Calculate the area under the curve using rectangles as their number becomes arbitrarily large (tends to infinity). You do not need to sketch the rectangles.

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

c. 6tan80

step-by-step explanation: