Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 16 - Multiple Integration - 16.2 Double Integrals over More General Regions - Exercises - Page 859: 43


$\cos (1)-\cos (2)$

Work Step by Step

The domain $D$ for given region can be expressed as: $1 \leq y \leq 2$ and $y \leq x \leq 2y$ The iterated integral can be calculated as: $\iint_{D} f(x,y) d A=\int_1^2 \int_{y}^{2y} \dfrac{\sin y}{y} \ dx \ dy\\=\int_1^2 (\dfrac{x \sin y}{y})_{y}^{2y} dy \\=\int_1^2 [2 \sin y -\sin y ) \ dy \\=\int_1^2 \sin y \ dy \\=[-\cos y]_1^2 \\=\cos (1)-\cos (2)$
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