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: 47



Work Step by Step

Formula to calculate the Flow is given by$ W=\int_C F(r(t)) \dfrac{dr}{dt}(dt)$ Here, $ \dfrac{dr}{dt}= i+2t j+0k$ Now, $\int_0^{2}(- 4t^3+8t^2 j+2k) (i+2t j+0 k)dt= \int_0^{2}(-4t^3)+(16t^3) dt$ Thus, $3[ (t)^4]_0^{2}=48$
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