Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 13: Vector-Valued Functions and Motion in Space - Practice Exercises - Page 777: 16



Work Step by Step

$v(t)=\dfrac{dr}{dt}=-3 \sin t i +3 \cos t j +3\sqrt t k$ and $|v(t)|=\sqrt {(-3 \sin t)^2 +(3 \cos t)^2 +(3\sqrt t)^2}=3 \sqrt {1+t}$ $Arc \ Length ( L)=\int_a^b |v| \ dt \\=\int_0^3 3 \sqrt {1+t} \ dt \\=[2(1+t)^{3/2}]_0^{3} \\=2(1+3)^{3/2} -2 \\ =14$
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