Question

Area enclosed 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 equal to

• A. $2$
• B. $4$
• C. $8$
• D. Cannot be determined

Answer 1

The correct option is B $4$

Required area = $2{\int }_0^1|log|x||dx$

$=2\left[\right(x|log|x||){]}_0^1-{\int }_0^1(-\frac{1}{2})xdx$

$=2\left[\right(1-0)+(x{)}_0^1]$

$=4sq.units$