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Comparing the Midpoint and Trapezoid Rules Apply the

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

Solution for problem 21E 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 21E

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 similar to Table 7.4 showing the approximations and errors for n = 4,8, 16, and 32.Step3 a=1 , b=5, n=4Using midpoint ruleStep4Midpoint sum for N=4++-------+)++-------+)=47.25Error for N=4 for midpoint rule===0.5275Step5Using midpoint ruleMidpoint sum for N=8++-------+)++-------+)=70.663Error for N=8 for midpoint rule===0.29337Step6Using midpoint ruleMidpoint sum for N=16++-------+)++-------+)=84.5513Error for N=16 for midpoint rule===0.154487=0.15449Step7Using midpoint ruleMidpoint sum for N=32++-------+)++-------+)=92.0769Error for N=32 for midpoint rule===0.079231Step8Table for midpoint approximation and errorNApproximationError447.250.5275870.6630.293371684.55130.154493292.07690.079231Step9N=4Using trapezoidal ruleTrapezoidal sum for N=4=102Error for N=4 for Trapezoidal rule===0.02Step10N=8Using trapezoidal ruleTrapezoidal sum for N=8=100.5Error for N=8 for Trapezoidal rule===0.005Step11N=16Using trapezoidal ruleTrapezoidal sum for N=16=100.125Error for N=16 for Trapezoidal rule===0.00125Step12N=32Using trapezoidal ruleTrapezoidal sum for N=32=100.0313Error for N=32 for Trapezoidal rule===0.000313Step 13Table for Trapezoidal approximation and errorNApproximationError41020.028100.50.00516100.1250.0012532100.03130.000313

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Chapter 7.6, Problem 21E is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

The full step-by-step solution to problem: 21E from chapter: 7.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. 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 21E from 7.6 chapter was answered, more than 338 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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