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Solved: Trapezoid Rule and Simpson’s Rule Consider the

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

Solution for problem 32E 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 32E

Trapezoid Rule and Simpson’s Rule

Consider the following integrals and the given values of n.

a. Find the Trapezoid Rule approximation to the integral using n and 2n subintervals.

b. Find the Simpson’s Rule approximation to the integral using 2n subintervals. It is easiest to obtain Simpson’s Rule approximations from the Trapezoid Rule approximations, as in Example 6.

c. Compute the absolute errors in the Trapezoid Rule and Simpson’s Rule with 2n subintervals.

Step-by-Step Solution:

Problem 32E

Trapezoid Rule and Simpson’s Rule Consider the following integrals and the given values of n.

a. Find the Trapezoid Rule approximation to the integral using n and 2n subintervals.

b. Find the Simpson’s Rule approximation to the integral using 2n subintervals. It is easiest to obtain Simpson’s Rule approximations from the Trapezoid Rule approximations, as in Example 6.

c. Compute the absolute errors in the Trapezoid Rule and Simpson’s Rule with 2n subintervals.

Step 1:

Given integral is

(a)Trapezoidal rule states that

We have  a=0, b=, n=30.

Therefore

Divide interval [0, into n=30 subintervals of length with the following endpoints

Now, we just evaluate function at those endpoints:

….

Finally, just sum up above values and multiply by

 

   

Answer : 

Step 2</p>

We have  a=0, b=, n=60.

Therefore

Divide interval [0, into n=60 subintervals of length with the following endpoints

Now, we just evaluate function at those endpoints:

….

Finally, just sum up above values and multiply by

                        

Answer :

Step 3 of 4

Chapter 7.6, Problem 32E is Solved
Step 4 of 4

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

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “Trapezoid Rule and Simpson’s Rule Consider the following integrals and the given values of n.a. Find the Trapezoid Rule approximation to the integral using n and 2n subintervals.b. Find the Simpson’s Rule approximation to the integral using 2n subintervals. It is easiest to obtain Simpson’s Rule approximations from the Trapezoid Rule approximations, as in Example 6.c. Compute the absolute errors in the Trapezoid Rule and Simpson’s Rule with 2n subintervals.” is broken down into a number of easy to follow steps, and 70 words. This full solution covers the following key subjects: rule, trapezoid, simpson, subintervals, Approximation. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Since the solution to 32E from 7.6 chapter was answered, more than 291 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 32E from chapter: 7.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.

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