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Midpoint Rule, Trapezoid Rule and relative error Find the

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

Solution for problem 19E 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 19E

Midpoint Rule, Trapezoid Rule and relative error

Find the Midpoint and Trapezoid Rule approximations to  sin πx dx using n = 25 subintervals. Compute the relative error of each approximation.

Step-by-Step Solution:

The actual value of

Step 1</p>

We have to approximate using both midpoint rule and trapezoidal rule by taking n=25.

And then we have to compute the relative error for both the approximations.

Step 2</p>

Mid point rule:

The general midpoint  rule is

Where the interval is  and  and are the midpoints for each interval.

Thus for the given question we get

And the subintervals will be

Therefore we have

………..

Therefore

 

The relative error  in this case is given by the equation

Step 3 of 3

Chapter 7.6, Problem 19E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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