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 - Preliminary Questions - Page 457: 4



Work Step by Step

Given $$\int_0^3f(x)dx,\ \ |f''(x)|=2 $$ Since the maximum error is $$ \left|f^{\prime \prime}(x)\right| \frac{(b-a)^{3}}{12 n^{2}}$$ Then \begin{align*} \left|f^{\prime \prime}(x)\right| \frac{(b-a)^{3}}{12 n^{2}}&\leq2 \frac{(3-0)^{3}}{12 (4)^{2}}\\ &=\leq 0.28125 \end{align*}
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