Question

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

• A. 4 sq. units
• B. 6 sq. units
• C. 10 sq. units
• D. None of these

Answer 1

Answer: (A)

4 sq. units

Required Area $=2{\int }_0^1\left|\log \left|x\right|\right|dx$
$=2{\left[\left(x\left|\log \left|x\right|\right|\right)\right]}_0^1-{\int }_0^1(-\frac{1}{x})xdx$
$=2[(1-0)+{\left(x\right)}_0^1]=4$ units