Question

The area bounded by the curves
$y=\ln x,y=\ln \left|x\right|,y=\left|\ln x\right|$ and $y=\left|\ln \left|x\right|\right|$ is

• A. $5$.sq.unit
• B. $2$.sq.unit
• C. $4$.sq.unit
• D. none of these

Answer 1

The correct option is C $4$.sq.unit

$\therefore$ Required area$=4{\int }_{-\infty }^0{e}^{y}dy$
$=4{\left[e^y\right]}_{-\infty }^0$
$=4[e^0-e^{-\infty }]$
$=4(1-0)=4$.sq.unit.