SOLUTION: Estimate the area under the curve y = X³ from 2 to 5 using left endpoints with 10 rectangles.

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Question 1112905: Estimate the area under the curve y = X³ from 2 to 5 using left endpoints with 10 rectangles.
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The calculations are straightforward; but this particular example is messy. If the problem was intended to give you practice with the solution method, then it is a lousy problem....

Dividing the interval from 2 to 5 into 10 intervals makes the left endpoints of the intervals
2, 2.3, 2.6, 2.9, 3.2, 3.5, 3.8, 4.1, 4.4, and 4.7.

The estimate of the area under the curve is the sum of the areas of the rectangles formed using those left endpoints and the function value at those endpoints. The width of each rectangle is the width of each interval (0.3); the length ("height") of each rectangle is the function y=x^3 evaluated at the left endpoint. So the estimate is



You can do the calculations... I don't think it is worth the time.
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