Thomas' Calculus 13th Edition

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

Chapter 16: Integrals and Vector Fields - Section 16.1 - Line Integrals - Exercises 16.1 - Page 943: 12


$80 \pi$

Work Step by Step

As we know that $ds=\sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2+(\dfrac{dz}{dt})^2} dt$ Here, $ds=\sqrt{(-4 \sin t)^2+( 4 \cos t )^2+(3)^2} dt$ or, $ds= \sqrt {25} dt=5 dt$ Line integral:$l=\int_C \sqrt{x^2+y^2} ds$ or, $\int_{-2 \pi}^{2 \pi} \sqrt {16 \cos ^2 t+16 \sin ^2 t} (5) dt=20(4 \pi)$ Thus, $l=\int_C \sqrt{x^2+y^2} ds=80 \pi$
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