Ta có: $\dfrac{\ln x}{2\sqrt x}=0 \Leftrightarrow x=1$
Diện tích hình phẳng cần tìm là:
$S=\int\limits_1^e|\dfrac{\ln x}{2\sqrt x}|dx$
$=\int\limits_1^e\dfrac{\ln x}{2\sqrt x}dx$
$=\int\limits_1^e\ln xd(\sqrt x)$
$=\sqrt x\ln x\left\{\begin{array}{l}e\\1\end{array}\right.-\int\limits_1^e\sqrt xd(\ln x)$
$=\sqrt e-\int\limits_1^e\dfrac{1}{\sqrt x}dx$
$=\sqrt e-2\sqrt x\left|\begin{array}{l}e\\1\end{array}\right.$
$=2-\sqrt e$