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Math Help - Approximating the Area of A Plane Region

  1. #1
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    Approximating the Area of A Plane Region

    Hello,

    I am reading an example problem in my text that is concerned with what is in the title of this thread. The given function f(x) = -x2 + 5, and the area that they want to find is within the interval [0, 2]. I am able to follow along when the author finds the area of the the area of under the graph from the inscribed rectangles, but when the author outlines the steps to find the area of the circumscribed rectangles I start to become uncertain as to what he is trying to do. He writes, "The left endpoints of the five intervals are 2/5(i - 1), where i = 1,2,3,4,5." He, of course, is using summation techniques to find the approximate area, but I just don't understand why the expression is (i -1).

    Thank you
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  2. #2
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    Re: Approximating the Area of A Plane Region

    Not sure why the question would arise with circumscribed but not inscribed, but anyway it makes sense to multiply 2/5 by i-1 for each of i = 1,2,3,4,5 because you're dividing up the interval [0,2] on the x axis into five intervals, beginning at 0, 2/5, 4/5, 6/5 and 8/5 respectively.
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