Thomas' Calculus 13th Edition

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

Chapter 15: Multiple Integrals - Practice Exercises - Page 933: 17


$\dfrac{1}{4} $

Work Step by Step

$$Average=\int_{0}^{1} \int_{0}^{1} xy \ dy \ dx \\=\int_{0}^{1} [\dfrac{xy^2}{2}]_0^1 \ dx \\=\int_{0}^{1} \dfrac{x}{2} \ dx \\= \int_{0}^{1} \dfrac{x}{2} \ dx \\=(\dfrac{1}{2}) [\dfrac{x^2}{2}]_0^1 \\=(\dfrac{1}{4}) (1-0) \\=\dfrac{1}{4} $$
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