## University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson

# Chapter 14 - Section 14.1 - Double and Iterated Integrals over Rectangles - Exercises - Page 759: 18

#### Answer

$4$

#### Work Step by Step

Re-arrange the given integral as follows: $\int_{-\pi}^{0} [(-y \cos (x+y)_{0}^{\pi} +\int_{0}^{\pi} \cos (x+y) dy] dx=\int_{-\pi}^{0} \pi \cos x-\sin x-\sin x dx$ This implies that $[\pi \sin x+\cos x+\cos x]_{-\pi}^{0}=(\pi \sin 0+\cos 0+\cos 0)-(\pi \sin \pi+\cos \pi+\cos \pi)$ Hence, $1+1+1+1=4$

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