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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.6 - Problem 56ae
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.6 - Problem 56ae

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Exact Trapezoid Rule Prove that the Trapezoid Rule is ISBN: 9780321570567 2

Solution for problem 56AE Chapter 7.6

Calculus: Early Transcendentals | 1st Edition

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Problem 56AE

Problem 56AE

Exact Trapezoid Rule

Prove that the Trapezoid Rule is exact (no error) when approximating the definite integral of a linear function.

Step-by-Step Solution:

SOLUTION

Step 1

The trapezoidal method error formula is given by for any in the interval . is the approximation of the definite integral using the trapezoidal rule .

A linear functions are those whose graph is a straight line.

A linear function is of the form Thus the second derivative of a linear function is always zero.

Therefore for a linear function becomes zero.

Thus  the Trapezoid Rule is exact (no error) when approximating the definite integral of a linear function.

Step 2 of 1

ISBN: 9780321570567

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Since the solution to 56AE from 7.6 chapter was answered, more than 392 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 56AE from chapter: 7.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: trapezoid, rule, exact, integral, function. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The answer to “Exact Trapezoid Rule Prove that the Trapezoid Rule is exact (no error) when approximating the definite integral of a linear function.” is broken down into a number of easy to follow steps, and 21 words.

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