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# Comparing the Midpoint and Trapezoid Rules Compare the ISBN: 9780321570567 2

## Solution for problem 40E Chapter 7.6

Calculus: Early Transcendentals | 1st Edition

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Problem 40E

Comparing the Midpoint and Trapezoid Rules

Compare the errors in the Midpoint and Trapezoid Rules with n =4, 8, 16, and 32 subintervals when they are applied to the following integrals (with their exact values given). Step-by-Step Solution:

Solution:-

Step1

Given that

Compare the errors in the Midpoint and Trapezoid Rules with n =4, 8, 16, and 32 subintervals

n = 4,8, 16, and 32

The exact values of the integrals are given for computing the error.  dx= 0.490874

Step2

To find

Compare the errors in the Midpoint and Trapezoid Rules with n =4, 8, 16, and 32 subintervals when they are applied to the following integrals (with their exact values given).

Step3

a=0 , b=1.5708, n=4

Using midpoint rule Step4

Midpoint sum for N=4  + +-------+ )  + +-------+ ) =0.490874

Error for N=4 for midpoint rule = = =1.348 Step5

Using midpoint rule Midpoint sum for N=8  + +-------+ )  + +-------+ ) =0.490874

Error for N=8 for midpoint rule = = =2.57919 Step6

Using midpoint rule Midpoint sum for N=16  + +-------+ )  + +-------+ ) =0.490874

Error for N=16 for midpoint rule = = =2.39792 Step7

Using midpoint rule Midpoint sum for N=32  + +-------+ )  + +-------+ ) =0.490874

Error for N=32 for midpoint rule = = =1.61971 Step8

N=4

Using trapezoidal rule Trapezoidal  sum for N=4   =0.490874

Error for N=4 for Trapezoidal  rule = = =2.3427 Step9

N=8

Using trapezoidal rule Trapezoidal  sum for N=8   =0.490874

Error for N=8 for Trapezoidal  rule = = =1.84535 Step10

N=16

Using trapezoidal rule Trapezoidal  sum for N=16   =0.490874

Error for N=16 for Trapezoidal  rule = = =1.05164 Step11

N=32

Using trapezoidal rule Trapezoidal  sum for N=32   =0.490874

Error for N=32 for Trapezoidal  rule = = =1.72478 Step 12</p>

Table for   approximation and error

 N Approximation (Midpoint Rule) Error(Midpoint Rule) Approximation (Trapezoidal Rule) Error(Trapezoidal Rule) 4 0.0490874
Step 7 of 12

Step 8 of 12

##### ISBN: 9780321570567

This full solution covers the following key subjects: midpoint, trapezoid, Rules, Integrals, exact. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 40E from 7.6 chapter was answered, more than 322 students have viewed the full step-by-step answer. The answer to “Comparing the Midpoint and Trapezoid Rules Compare the errors in the Midpoint and Trapezoid Rules with n =4, 8, 16, and 32 subintervals when they are applied to the following integrals (with their exact values given).” is broken down into a number of easy to follow steps, and 36 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 40E from chapter: 7.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.

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