Answer
$$4\sqrt{13}.$$
Work Step by Step
We have $r(t) =2ti-3tk$, and so $r'(t) =2i-3k$.
We calculate the length by integration:
$$length=\int_{11}^{15}\sqrt{4+9}dt=\sqrt{13}t|_{11}^{15}=4\sqrt{13}.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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