Chapter 7: Transcendental Functions - Practice Exercises - Page 441: 117

$A$ = $1$

$A$ = $\int_{{\,1}}^{{\,e}}$ $ \frac{2\ln{x}}{x}$ $dx$ $u$ = $\ln{x}$ $du$ = $\frac{1}{x}dx$ $x$ = $1$ then $u$ = $0$ $x$ = $e$ then $u$ = $1$ $A$ = $\int_{{\,0}}^{{\,1}}$ $2u$ $du$ $A$ = $u^{2}$ $|_{{\,0}}^{{\,1}}$ $A$ = $1$