Question

The area of the region of the plane bounded by $(\left|x\right|,\left|y\right|)\le 1\&xy\le \frac{1}{2}$ is

• A. less than $4ln3$
• B. $\frac{15}{4}$
• C. $2+2ln2$
• D. $3+ln2$

Answer 1

Answer: (A), (D)

The correct options are
A less than $4ln3$
D $3+ln2$

${\Delta }_2={\Delta }_1={\int }_{1/2}^1[1-\frac{1}{2x}]dx=\frac{1}{2}-\frac{1}{2}ln2$
$A=4-({\Delta }_1+{\Delta }_2)=4-(1-ln2)=3+ln2$