Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 11 - Vectors and Vector-Valued Functions - 11.6 Calculus of Vector-Valued Functions - 11.6 Exercises: 50

Answer

$\int\textbf{r}(t) dt = \langle te^{-t}-e^t, \frac{-1}{2}cos(t^2), -2\sqrt {t^2+4}\rangle + C$

Work Step by Step

To find the indefinite integral, compute the integral of each component. $\int\textbf{r}(t) dt = \langle \int te^t\ dt,\int t\ sin(t^2)\ dt,\int \frac{-2t}{\sqrt {t^2 + 4}}\ dt\rangle = \langle te^{-t}-e^t, \frac{-1}{2}cos(t^2), -2\sqrt {t^2+4}\rangle + C$
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