University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.10 - The Binomial Series and Applications of Taylor Series - Exercises - Page 549: 23


$$| Error| \lt 0.00011$$

Work Step by Step

We integrate the integral with respect to $ x $ taking a lower limit as $0$ and upper limit as $1$. $\int_0^{1} \cos t^2 dt=\int_0^{1} [1-\dfrac{t^2}{2}+\dfrac{t^{8}}{4 !}-...] dx $ or, $=[t-\dfrac{t^5}{10}+\dfrac{t^{9}}{9 \cdot 4 !}-...]_0^{10} ....$ So, the error can be calculated as: $| Error| \lt \dfrac{1}{13 \cdot 6 !} \approx 0.00011$
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