Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 441: 37

Answer

$-1$

Work Step by Step

$\int_R^1{\ln{x}dx}$ = $x\ln{x}|_R^1$ = $R-1-R\ln{R}$ $\int_0^1{\ln{x}dx}$ = $\lim\limits_{R \to {0^{+}}}$$(R-1-R\ln{R})$ = $-1-\lim\limits_{R \to {0^{+}}}(R\ln{R})$ = $-1$
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