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Improper integrals by numerical methods Use the Trapezoid

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

Solution for problem 51E Chapter 7.7

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 51E

Improper integrals by numerical methods Use the Trapezoid Rule (Section 7.6) to approximate  with R =2, 4, and 8. For each value of R, take n = 4, 8, 16, and 32, and compare approximations with successive values of n. Use these approximations to approximate .

Step-by-Step Solution:
Step 1 of 3

Solution:-

Step1

Given that

Use the Trapezoid Rule (Section 7.6) to approximate  with R =2, 4, and 8. For each value of R, take n = 4, 8, 16, and 32, . Use these approximations to approximate .

Step2

To find

compare approximations with successive values of n.

Step3

N=4 and R=2

Using trapezoidal rule

Divide interval [0,2] into n=4 subintervals of length

a=0,

f(

2f(

2f(

2f(

f(

Finally , just sum up above values and multiply by

=

=

Step4

N=8 and R=4

Using trapezoidal rule

Divide interval [0,4] into n=8 subintervals of length

a=0,

f(

2f(

2f(

2f(

2f(

2f(

2f(

2f(

f(

Finally , just sum up above values and multiply by

=

=0.886227

Step5

N=16 and R=8

Using trapezoidal rule

Divide interval [0,8] into n=16 subintervals of length

a=0,

f(

2f(

2f(

2f(

.

.

.

.

2f(

f(

Finally , just sum up above values and multiply by

=

=0.886227

Step 2 of 3

Chapter 7.7, Problem 51E is Solved
Step 3 of 3

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

The answer to “Improper integrals by numerical methods Use the Trapezoid Rule (Section 7.6) to approximate with R =2, 4, and 8. For each value of R, take n = 4, 8, 16, and 32, and compare approximations with successive values of n. Use these approximations to approximate .” is broken down into a number of easy to follow steps, and 46 words. Since the solution to 51E from 7.7 chapter was answered, more than 306 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: approximate, approximations, use, numerical, Integrals. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 51E from chapter: 7.7 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.

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