question_answer

The area bounded by the curves y = ln x, y = ln \[\left| x \right|,y=\left| ln\text{ }x \right|\] and \[,y=\left| ln\text{ }\left| x \right| \right|\] is

A) 4 sq. units

B) 6 sq. units

C) 10 sq. units

D) None of these

Correct Answer: A

Solution :

[a] First we draw each curve as separate graph Clearly the bounded area is as shown in the following figure. Required area \[=4\int\limits_{0}^{1}{(-\ell nx)dx}\] \[=-4\,[x\ell n\,x-x]_{0}^{1}=4\] sq. units