MTH 162 Lecture Notes - Lecture 13: Riemann Sum

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19 May 2017
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Provide a generalization to each of the key terms listed in this section. What is the midpoint rule: the midpoint rule is used to approximate the area that"s under the function along with the x-axis thanks to subdividing the area into rectangles. When it comes to the midpoint rule, to help approximate r b a f (x) dx, then it would be best to use the following where [a, b] is partitioned into n subintervals with of equivalent length, which is. 2 (cid:19) + f (cid:18) x1 + x2. 2 (cid:19) + + f (cid:18) xn 1 + xn. By using 4 rectangles, use the midpoint rule to estimate r 3. 2 +2 f (cid:0) x0+x1 f (cid:0) x1+x2 f (cid:0) x2+x3 f (cid:0) x3+x4 (cid:1) = f (cid:16) 1+ 3 (cid:1) = f (cid:16) 3 (cid:1) = f (cid:16) 2+ 5 (cid:1) = f (cid:16) 5.

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