Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
8th Edition
ISBN: 9781305279148
Author: Stewart, James, St. Andre, Richard
Publisher: Cengage Learning
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Chapter 5.2, Problem 3PT
To determine

To choose: The appropriate option for the Riemann sum of 17x2dx by using n=4 and midpoints for xi*.

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Use geometry (not Riemann sums) to compute the integral.   3   0 x dx
Use Riemann sums and a limit to compute the exact area under the curve ? = ?(?) = 2x2 + 1 on the interval [1, 3].
Explain why both the Riemann sum R(f,P) and )f b/a ffall between L(f,P) and U(f,P). (b) Explain why U(f,P1) − L(f,P1) < /3. By the previous exercise, if we can show U(f,P) < U(f,P) + /3 (andsimilarly L(f,P) − /3 < L(f,P)), then it will follow that and the proof will be done. Thus, we turn our attention toward estimating thedistance between U(f,P) and U(f,P).
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