Calculus (3rd Edition)

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

Chapter 14 - Calculus of Vector-Valued Functions - 14.2 Calculus of Vector-Valued Functions - Exercises - Page 720: 45


$\left\langle\ln 4, \frac{56}{3 }, -\frac{496}{5 } \right\rangle.$

Work Step by Step

We have \begin{align} \int_{1}^{4}\left\langle t^{-1},4 t^{1/2}, -8 t^{3/2} \right\rangle dt &=\left\langle \ln t, \frac{4}{3/2} t^{3/2},-\frac{8}{5/2} t^{5/2} \right\rangle|_{1}^{4}\\ &=\left\langle \ln 4, \frac{8}{3} 4^{3/2},-\frac{16}{5} 4^{5/2}\right\rangle-\left\langle 0, \frac{8}{3} ,-\frac{16}{5} \right\rangle\\ &=\left\langle\ln 4, \frac{56}{3 }, -\frac{496}{5 } \right\rangle. \end{align}
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