SOLUTION: 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

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Question 1177659: 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 10 rectangles to approximate the area under the curve.

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
Sketch the graph of the function



divide the area in rectangles


In order to figure the width of each rectangle we can use the following formula:
Δ
in this case , and so we get:
Δ
so rectangle must have a of units
We can now calculate the height of each rectangle. So we figure the y-value of each corner of the rectangles. We get the following heights:
..........units->
..............units->
.............units->...and so on







so now we can use the following formula to find the area under the graph. Basically what the formula does is add the areas of the rectangles:


-> approximate the area under the curve in the interval [, ]

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