Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 16 - Vector Calculus - 16.2 Line Integrals - 16.2 Exercises - Page 1126: 44


$\dfrac{m(b^2-a^2)}{2} $

Work Step by Step

Work done$W=\int_C F\cdot dr=\int_C F\cdot r'(t) dt=\int_0^{\pi/2} (-ma \sin t i-mb \cos t j) \cdot (a \cos t i-b \sin t j+ck) dt$ $=m (b^2-a^2) \int_0^{\pi/2} (\sin t) \times (\cos t) dt$ $=\dfrac{m(b^2-a^2)}{2} \int_0^{\pi/2} \sin (2 t) dt $ $=\dfrac{m(b^2-a^2)}{2} \times [\dfrac{-\cos (2t) }{2}]_0^{\pi/2}$ $=\dfrac{m(b^2-a^2)}{2}\times (\dfrac{1-(-1)}{2})$ $=\dfrac{m(b^2-a^2)}{2}\times (\dfrac{2}{2})$ $=\dfrac{m(b^2-a^2)}{2} $
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