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Unformatted text preview: ment, the approximation whould be much better. Lets choose a partition, such that the base of the rectangle is of length 1 100 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 2 4 6 8 10 12 14 16 x y We can see, that the sum of the area of the approximating rectangles is "close" compared to the previous re&nement. Since the curve is decreasing by choosing the left endpoint of the interval, the sum of the areas of the approximating rectangles, is greater that the actual area. 1 100 400 X k =1 " 16 & & k & 1 100 ± 2 # = 213 733 5000 ± 42 : 746 6 We will explain in the next couple of sections, how to calculate the actual area, which is A = 128 3 ± 42 : 666 666 666 666 666 667 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 2 4 6 8 10 12 14 16 x y 4...
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 Spring '12
 kaint
 Math, Angles, Rectangle, left endpoint

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