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 882: 25


$\dfrac{3 \ln 2}{2}$

Work Step by Step

Consider: $I= \iint_{R} f(x,y) dA$ or, $= \int_{1}^{2} \int_{x}^{2x} xy^{-1} dy dx$ or, $= \int_{1}^{2}[x \ln (y) ]_x^{2x}$ or, $=\int_{1}^{2} x \ln (2x)- x \ln x dx$ Thus, we have $I=\int_1^{2} \ln 2 x dx=\dfrac{3 \ln 2}{2}$
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