Answer
$\frac{\pi}{4}$
Work Step by Step
$\int_CF.dr=\int_0^{\pi}(1+t)sintcostdt+\int_0^{\pi}sin^2tdt$
$=[\frac{-1}{2}(1+t)cos2t+\frac{sin2t}{4}]_0^{\pi}+[\frac{t}{2}-\frac{sin2t}{4}]_0^{\pi}$
$=-\frac{\pi}{4}+\frac{\pi}{2}$
$=\frac{\pi}{4}$
Multivariable Calculus, 7th Edition
by Stewart, James
Published by
Brooks Cole
ISBN 10:
0-53849-787-4
ISBN 13:
978-0-53849-787-9
Chapter 16 - Vector Calculus - Review - Exercises - Page 1161: 8
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