Answer
$48$
Work Step by Step
Flow $=\int_C F(r(t)) \dfrac{dr}{dt}(dt)$
and $ \dfrac{dr}{dt}= i+2t j+0 k$
Then , flow $=\int_0^{2}(- 4t^3+8t^2 j+2k) (i+2t j+0 k)dt$
or, $= \int_0^{2}-4t^3+16t^3+0 dt$
or, $=[ 3t^4]_0^{2}$
or, $=48$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 15 - Section 15.2 - Vector Fields and Line Integrals: Work, Circulation, and Flux - Exercises - Page 840: 47
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