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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.6 - Problem 41e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.6 - Problem 41e

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

## Solution for problem 41E Chapter 7.6

Calculus: Early Transcendentals | 1st Edition

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Problem 41E

Problem 41E

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= 0.406349

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  + +-------+ )  + +-------+ ) =0.406349

Error for N=4 for midpoint rule = = =1.46785 Step5

Using midpoint rule Midpoint sum for N=8  + +-------+ )  + +-------+ ) =0.406349

Error for N=8 for midpoint rule = = =1.95089 Step6

Using midpoint rule Midpoint sum for N=16  + +-------+ )  + +-------+ ) =0.406349

Error for N=16 for midpoint rule = = =2.66639 Step7

Using midpoint rule Midpoint sum for N=32  + +-------+ )  + +-------+ ) =0.406349

Error for N=32 for midpoint rule = = =2.28637 Step8

N=4

Using trapezoidal rule Trapezoidal  sum for N=4   =0.406349

Error for N=4 for trapezoidal rule = = =1.18341 Step9

N=8

Using trapezoidal rule Trapezoidal  sum for N=8   =0.406349

Error for N=8 for trapezoidal rule = = =1.4222 Step10

N=16

Using trapezoidal rule Trapezoidal  sum for N=16   =0.406349

Error for N=16 for trapezoidal rule = = =1.68655 Step11

N=32

Using trapezoidal rule Trapezoidal  sum for N=32   =0.406349

Error for N=32 for trapezoidal rule = = =2.17647 Step 12

Table for   approximation and error

 N Approximation (Midpoint Rule) Error(Midpoint Rule) Approximation (Trapezoidal Rule) Error(Trapezoidal Rule)
Step 2 of 12

Step 3 of 12

##### ISBN: 9780321570567

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