Answer
$\dfrac{-\pi}{2}$
Work Step by Step
Given: $\int_C F \cdot T ds-\int_C F. dr$
Now,
$\int_C y dx-x dy=\int_{0}^{\pi/2}(\sin t) (-\sin t dt) -(\cos t) (\cos t dt)=\int_{0}^{\pi/2} (-1) dt$
Thus, $\int_C y dx-x dy=\dfrac{-\pi}{2}$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
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 - Exercises 16.2 - Page 955: 26
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