The area bounded by the curves $$y = \ell n\,x,\,y = \ell n\left| x \right|,\,y = \left| {\ell n\,x} \right|$$       and $$y = \left| {\ell n\left| x \right|} \right|$$   is :

Solution :
First we draw each curve as separate graph

Clearly the bounded area is as shown in the following figure.

Required area
$$\eqalign{ & = 4\int\limits_0^1 {\left( { - \ell n\,x} \right)} dx \cr & = - 4\left[ {x\,\ell n\,x - x} \right]_0^1 \cr & = 4{\text{ sq}}{\text{. units}} \cr} $$