MAT136H1 Lecture : Overview

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MAT136H1 Full Course Notes
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Using the left endpoints, the area approximation is: . Using the right endpoints, the area approximation is: . Using the midpoints, the area approximation is: . , where is the midpoint of each subinterval [ ], so that . This represents the sum of rectangles of equal width under the curve over the interval [ ]. As the number of rectangles increase, the sum of the areas gets closer to true area under . When a function is consistently increasing over the interval: When a function is consistently decreasing over the interval: Midpoints always give the best estimate than the left endpoints or the right endpoints. Usually the variable represents the time element.

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