University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 5 - Practice Exercises - Page 343: 95



Work Step by Step

$$A=\int^4_1\Big(\frac{x}{8}+\frac{1}{2x}\Big)dx$$ $$A=\frac{1}{8}\int^4_1xdx+\frac{1}{2}\int^4_1\frac{1}{x}dx$$ $$A=\frac{1}{8}\times\frac{x^2}{2}\Big]^4_1+\frac{1}{2}(\ln|x|)\Big]^4_1$$ $$A=\frac{x^2}{16}\Big]^4_1+\frac{1}{2}(\ln4-\ln1)$$ $$A=\frac{16}{16}-\frac{1}{16}+\frac{\ln4-0}{2}$$ $$A=\frac{\ln4}{2}+\frac{15}{16}$$ $$A=\ln2+\frac{15}{16}$$
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