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: 48


\begin{align} r(t)&= \left\langle t+2,-t, 3 \right\rangle . \end{align}

Work Step by Step

By integration, we have \begin{align} r(t)&=\int r'(t) dt\\ &=\int \left\langle1,-1,0 \right\rangle dt\\&= \left\langle t+c_1,-t+c_2,c_3 \right\rangle . \end{align} By the condition $r(0)=\lt 2,0,3\gt$, we get $$2=c_1, \quad 0=c_2, \quad 3=c_3$$ Hence, we have \begin{align} r(t)&= \left\langle t+2,-t, 3 \right\rangle . \end{align}
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