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: 48



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}= 3 j+4 k$ Now, $\int_0^{1}(12t^2 j+9t^2 k) (3 j+4 k)dt= \int_0^{1}(36t^2)+(36t^2) dt$ Thus, $24[t^3]_0^{1}=24$
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