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Solved: Comparing the Midpoint and Trapezoid Rules Apply

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 22E Chapter 7.6

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 22E

Comparing the Midpoint and Trapezoid Rules Apply the Midpoint and Trapezoid Rules to the following integrals. Make a table similar to Table 7.4 showing the approximations and errors for n = 4,8, 16, and 32. The exact values of the integrals are given for computing the error.

Step-by-Step Solution:

Solution:-Step1Given thatApply the Midpoint and Trapezoid Rules to the following integrals.n = 4,8, 16, and 32The exact values of the integrals are given for computing the error. Step2To find Make a table showing the approximations and errors for n = 4,8, 16, and 32.Step3 a=-2 , b=6, n=4Using midpoint ruleStep4Midpoint sum for N=4++-------+)++-------+)=-2.624Error for N=4 for midpoint rule===1.656Step5Using midpoint ruleMidpoint sum for N=8++-------+)++-------+)=-1.1483Error for N=8 for midpoint rule===1.2871Step6Using midpoint ruleMidpoint sum for N=16++-------+)++-------+)=0.8719Error for N=16 for midpoint rule===0.78202Step7Using midpoint ruleMidpoint sum for N=32++-------+)++-------+)=2.2843Error for N=32 for midpoint rule==0.42893Step8Table for midpoint approximation and errorNApproximationError4-2.6241.6568-1.14831.2871160.87190.78202322.28430.42893Step9N=4Using trapezoidal ruleTrapezoidal sum for N=4=6Error for N=4 for Trapezoidal rule==0.5Step10N=8Using trapezoidal ruleTrapezoidal sum for N=8=4.5Error for N=8 for Trapezoidal rule==0.125Step11N=16Using trapezoidal ruleTrapezoidal sum for N=16=4.125Error for N=16 for Trapezoidal rule==0.03125Step12N=32Using trapezoidal ruleTrapezoidal sum for N=32=4.0313Error for N=32 for Trapezoidal rule==0.0078125Step 13Table for Trapezoidal approximation and errorNApproximationError460.584.50.125164.1250.03125324.03130.0078125

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Chapter 7.6, Problem 22E is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: Integrals, trapezoid, Table, Rules, midpoint. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The answer to “Comparing the Midpoint and Trapezoid Rules Apply the Midpoint and Trapezoid Rules to the following integrals. Make a table similar to Table 7.4 showing the approximations and errors for n = 4,8, 16, and 32. The exact values of the integrals are given for computing the error.” is broken down into a number of easy to follow steps, and 47 words. Since the solution to 22E from 7.6 chapter was answered, more than 317 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 22E from chapter: 7.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.

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Solved: Comparing the Midpoint and Trapezoid Rules Apply