×
Log in to StudySoup
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.6 - Problem 41e
Join StudySoup for FREE
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.6 - Problem 41e

Already have an account? Login here
×
Reset your password

Solution: Comparing the Midpoint and Trapezoid Rules Compare

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

Solution for problem 41E Chapter 7.6

Calculus: Early Transcendentals | 1st Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

4 5 1 377 Reviews
29
0
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

Chapter 7.6, Problem 41E is Solved
Step 3 of 12

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Solution: Comparing the Midpoint and Trapezoid Rules Compare