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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.6 - Problem 58ae
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.6 - Problem 58ae

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Shortcut for the Trapezoid Rule Prove that if you have

ISBN: 9780321570567 2

Solution for problem 58AE Chapter 7.6

Calculus: Early Transcendentals | 1st Edition

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Problem 58AE

Problem 58AE

Shortcut for the Trapezoid Rule

Prove that if you have M(n)and T(n)(a Midpoint Rule approximation and a Trapezoid Rule approximation with n subintervals), then T(2n) = (T(n) + M(n))/2.

Step-by-Step Solution:
Step 1 of 3

Solution:-

Step1

Given that

A Midpoint Rule approximation and a Trapezoid Rule approximation with n subintervals.

Step2

Prove that

Step3

The Midpoint Rule is the approximation of

+-------+]

The Trapezoidal  Rule is the approximation of

2+-------+]

We can divide the interval [a,b] into 2n equally spaced , we get

+-------+]

And

So, using the midpoint formula this become

2+-------+]

Similarly, The Trapezoidal  Rule may be written as

2+-------+]

Multiply both by and add we get

2+-------+]

And using the definition of Trapezoidal  Rule we find

=

Hence,

Proved

Step 2 of 3

Step 3 of 3

ISBN: 9780321570567

This full solution covers the following key subjects: rule, Approximation, trapezoid, shortcut, midpoint. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 58AE from chapter: 7.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “Shortcut for the Trapezoid Rule Prove that if you have M(n)and T(n)(a Midpoint Rule approximation and a Trapezoid Rule approximation with n subintervals), then T(2n) = (T(n) + M(n))/2.” is broken down into a number of easy to follow steps, and 29 words. Since the solution to 58AE from 7.6 chapter was answered, more than 331 students have viewed the full step-by-step answer.

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