Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 14 - Multiple Integrals - 14.1 Double Integrals - Exercises Set 14.1 - Page 1007: 5

Answer

$$\int_{0}^{\ln 3} \int_{0}^{\ln 2} e^{x+y} d y d x=2$$

Work Step by Step

Given $$\int_{0}^{\ln 3} \int_{0}^{\ln 2} e^{x+y} d y d x$$ So, we get \begin{aligned} I& = \int_{0}^{\ln 3} \int_{0}^{\ln 2} e^{x} \cdot e^{y} d y d x \\&= \int_{0}^{\ln 3} e^{x} d x \int_{0}^{\ln 2} e^{x} d y \\ & = \left[e^{x}\right]_{0}^{\ln 3}\left[e^{y}\right]_{0}^{\ln 2} \\&= \left[e^{\ln 3}-e^{0}\right]\left[e^{\ln 2}-e^{0}\right] \\ &=[3-1][2-1]=2 \end{aligned}
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