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 16.2 - Vector Fields and Line Integrals: Work, Circulation, and Flux - Page 957: 50



Work Step by Step

Formula to calculate the flow is given by: $\int_C F(r(t)) \dfrac{dr}{dt}(dt)$ Here, $ \dfrac{dr}{dt}=2 \sin t i+2 \cos t j+2k$ Now, $\int_0^{2 \pi}(-2 \sin t i -2 \cos t j+2k) (2 \sin t i+2 \cos t j+2k)=[-4+4 ]_0^{2 \pi}$ Thus, $=0$
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