Thomas' Calculus 13th Edition

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

Chapter 7: Transcendental Functions - Section 7.2 - Natural Logarithms - Exercises 7.2 - Page 381: 71


$4\ln 2\approx 2.773$

Work Step by Step

Area between curves $f(x)$ and $g(x)$, where $g(x)\geq f(x)$ on $[a,b], $ is $\displaystyle \int_{a}^{b}[g(x)-f(x)]dx=\int_{1}^{5}(\ln 2x-\ln x)dx\qquad $... $(\ln MN=\ln M+\ln N)$ $=\displaystyle \int_{1}^{5}(\ln 2+\ln x-\ln x)dx$ $=\int_{1}^{5}(\displaystyle \ln 2)dx$ $=\ln 2\cdot [x]_{1}^{5}$ $=\ln 2\cdot(5-1)$ $=4\ln 2$
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