Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.9 Numerical Integration - Exercises - Page 459: 57


Error $(S_2)=0$, so $S_2$ gives the exact value of the integral.

Work Step by Step

Error $(S_N) \leq \dfrac{k_4(b-a)^3}{180N^4} $ For $N=2$, we have: Error $(S_N) \leq \dfrac{k_4(b-a)^3}{180N^4} \\ \leq \dfrac{(0)(1-0)^3}{180(2)^4} \\ \leq 0$ The actual error is approximately $[121.5000006-121.5 ] \approx 6 \times 10^{-7} $, which is less than $10^{-6}$. We see that: Error $(S_2)=0$ So, $S_2$ gives the exact value of the integral.
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