Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 15 - Review - Exercises - Page 1062: 19

Answer

$\frac{1}{2}sin(1)$

Work Step by Step

Given: $\int_{0}^{1}\int_{x}^{1}cos(y^{2})dydx$ Integrate by switching order of integration. Since, $x=1$ and $x=0$ , putting this into $ y=x$ we get $y=0, y=1$ ,$x=y$, $x=0$ $=\int_{0}^{1}\int_{0}^{y}cos(y^{2})dxdy$ $=\int_{0}^{1}xcos(y^{2})|_{0}^{y}dy$ $=\int_{0}^{1}[ycos(y^{2})-0]|dy$ $=\frac{1}{2}sin(y^{2})|_{0}^{1}$ $=\frac{1}{2}sin(1)$
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