Calculus 8th Edition

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

Chapter 16 - Vector Calculus - Review - Exercises - Page 1189: 10


(a) $$\dfrac{3(\pi-3)}{2}$$ (b) $$-\dfrac{3\pi}{4}$$

Work Step by Step

(a) Work done$=\int_CF.dr$ $=\int_0^{1}(3ti+(-3t+3)j+\frac{\pi t}{2}k)(-3i+\frac{\pi }{2}j+3k)dt$ $=\int_0^{1}(-9t+3\pi/2)dt$ $=[-\dfrac{9t^2}{2}+\dfrac{3 \pi t}{2}]_0^{1}$ $=-\frac{9}{2}+\frac{3 \pi}{2}$ $=\dfrac{3(\pi-3)}{2}$ (b) Work done$=\int_CF.dr$ $=\int_0^{\pi/2}(3sinti+3costj+tk))(-3sinti+j+3costk)dt$ $=\int_0^{\pi/2}(-9sin^2t+3cost+3tcost)dt$ $=\frac{-9\pi}{4}+3+(\frac{3 \pi}{2}-3)$ $=-\dfrac{3\pi}{4}$
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