Thank you for reporting, we will resolve it shortly
Q.
The area of the region of the plane bounded by $(|x|,|y|) \leq 1 \& x y \leq \frac{1}{2}$ is :
Application of Integrals
Solution:
shaded area in $1^{\text {st }}$ quadrant is to be excluded from the area of the square of side 2
$\left.=\int\limits_{1 / 2}^1\left(1-\frac{1}{2 x }\right) dx = x -\frac{1}{2} \ln x \right]_{1 / 2}^1 $
$=\frac{1}{2}+\frac{1}{2} \ln \frac{1}{2}=\frac{1}{2}-\frac{1}{2} \ln \frac{1}{2}$
$\therefore 2 \text { times the shaded area }=1-\ln 2 $
$\therefore \text { Required area }=2-(1-\ln 2)+2=3+\ln 2 \Rightarrow D$
