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 - 14.3 Arc Length and Speed - Exercises - Page 725: 2



Work Step by Step

We have $r(t) =2ti-3tk$, and so $r'(t) =2i-3k$. We calculate the length by integration: $$length=\int_{11}^{15}\sqrt{4+9}dt=\sqrt{13}t|_{11}^{15}=4\sqrt{13}.$$
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