How to improve the accuracy of the approximation for the area under a curve?
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To find the area under a curve we approximate the area using rectangles and then use limits to find the area. Example 1 Suppose we want to estimate A = the area under the curve y = 1 − x2, 0 ≤ x ≤ 1. [0,1/4], [1/4,1/2], [1/2,3/4],[3/4,1] each with length ∆x = 1/4.
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