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. units
B
6 sq. units
C
10 sq. units
D
None of these
Answer
4 sq. units
Explanation
Solution
Note that ln x is defined for x > 0 and ln | x | is defined for | x | > 0. Also, | ln x | ³ 0 and also | ln | | x | = | ln | x | | ³ 0.
Required area is symmetrical in all the four quadrants and is equal to 4
dx = – 4
[In (0, 1), ln x < 0]
= –4 [x ln x – x
= – 4 (–1) = 4.
(Q
x ln x = 0)