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: 33


$1-\cos (1)$

Work Step by Step

The domain $D$ for given region can be expressed as: $0 \leq y \leq x$ and $0 \leq x \leq 1$ The iterated integral can be calculated as: $\iint_{D} f(x,y) d A= \int_{0}^{1} \int_{0}^{x} \dfrac{\sin x}{x} \ dy \ dx \\= \int_{0}^{1} [\dfrac{\sin x}{x} \times y]_0^x \ dx\\= \int_{0}^{1} (\sin x-0) \ dx \\= [-\cos x]_0^1\\=-\cos (1)+\cos (0) \\=1-\cos (1)$
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