Answer: Comparing the Midpoint and Trapezoid Rules Compare

Chapter 5, Problem 42E

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QUESTION:

Comparing the Midpoint and Trapezoid Rules  Compare the errors in the Midpoint and Trapezoid Rules with n=4, 8, 16, and 32 subintervals when they are applied to the following integrals (with their exact values given).

\(\int_{0}^{1}\left(8 x^{7}-7 x^{8}\right) d x=\frac{2}{9}\)

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QUESTION:

Comparing the Midpoint and Trapezoid Rules  Compare the errors in the Midpoint and Trapezoid Rules with n=4, 8, 16, and 32 subintervals when they are applied to the following integrals (with their exact values given).

\(\int_{0}^{1}\left(8 x^{7}-7 x^{8}\right) d x=\frac{2}{9}\)

ANSWER:

Step 1 of 12

Given that

Compare the errors in the Midpoint and Trapezoid Rules with n =4, 8, 16, and 32 subintervals

n = 4,8, 16, and 32

The exact values of the integrals are given for computing the error.

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