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: 49



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}=- \sin t i+0j+\cos tk$ Now, $\int_0^{\pi}(- \sin t i+0j+\cos tk)((\cos t- \sin t) i+0j+\cos tk) dt= \int_0^{\pi}(\dfrac{-1}{2})( \sin 2t )+1 dt$ Thus, $[ (\dfrac{1}{4}) (\cos 2t) +t]_0^{\pi}=\pi$
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