Question 1206935: Use upper rectangles with areas equal to f(x). Ax to estimate the area under the curve of f(x) = x², on the interval [0,2]. Partition the interval into 8 subintervals
Answer by greenestamps(13209)   (Show Source):
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The function f(x)=x^2 is monotonically increasing on the interval [0,2], so the heights of all of the upper rectangles will be the function values at the upper ends of the intervals.
With 8 subintervals on [0,2], the width of each rectangle will be 2/8 = 1/4.
The upper endpoints of the 8 intervals are 1/4, 2/4, 3/4, 4/4, 5/4, 6/4, 7/4, and 8/4.
The function values at those endpoints -- i.e., the heights of the rectangles -- are 1/16, 4/16, 9/16, 16/16, 25/16, 36/16, 49/16, and 64/16.
The sum of the areas of the eight rectangles is
ANSWER: 51/16
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