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: 25


$| Error| \lt 0.000013$

Work Step by Step

We integrate the integral with respect to $ x $ taken a lower limit as $0$ and upper limit as $1$. $ f(x)=\int_0^{x} \sin t^2 dt=\int_0^{x} [t^2-\dfrac{t^6}{3 !}+\dfrac{t^{10}}{5!}-...] dt $ or, $=\dfrac{x^3}{3}-\dfrac{x^{7}}{7 \cdot 3 !}+\dfrac{x^{11}}{11 \cdot 5!}- ....$ So, the error can be calculated as: $| Error| \lt \dfrac{1}{15\cdot 7 !} \approx 0.000013$
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