Exact Trapezoid Rule
Prove that the Trapezoid Rule is exact (no error) when approximating the definite integral of a linear function.
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.
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
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.