Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 15: Multiple Integrals - Section 15.2 - Double Integrals over General Regions - Exercises 15.2 - Page 883: 53


$\dfrac{1}{80 \pi}$

Work Step by Step

We reverse the order of integration to get: $I= \int_0^{1/2} \int_0^{x^4} \cos (16 \pi x^5)dy dx$ or, $= \int_0^{1/2} x^4 \cos (16 \pi x^5) dx$ Set $a = 16 \pi x^5 \implies da=80 \pi x^4 dx$ Now, $I=\dfrac{1}{80} \int_0^{5 \pi/2} \cos a da=\dfrac{1}{80 \pi}$
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