Question
Question: The area bounded by the curves y = ln x, y = ln \|x\|, y = \|ln x\| and y = \|ln\|x\|\| is -...
The area bounded by the curves y = ln x, y = ln |x|, y = |ln x| and y = |ln|x|| is -
A
4 sq unit
B
6 sq unit
C
10 sq unit
D
None
Answer
4 sq unit
Explanation
Solution
log x is defined for x > 0
log |x| is defined for x Î R – {0}
Also |log x| ³ 0 & | log |x|| ³ 0
Required area is symmetrical in all four quadrants. So, Required area = 4 
= – 4 
[in (0,1), log x < 0]
= – 4 [– 1] = 4 sq. unit