12th Class
Mathematics
Definite Integrals
Question Bank
Critical Thinking
question_answer
The area bounded by the curves \[y=\ln x\], \[y=\ln |x|\], \[y=\,|\ln x|\] and \[y=\,|\ln |x||\] is [AIEEE 2002]
A)4 sq. unit
B)6 sq. unit
C)10 sq. unit
D)None of these
Correct Answer:
A
Solution :
We know that \[\log x\] is defined for \[x>0\] and \[\log |x|\] is defined for all \[x\in R-\{0\}\]
Also \[|\log x|\ge 0\] and \[|\log \,|x|\,|\,\ge \,0\]
\[\therefore \]Required area is symmetrical in all the four quadrants and is equal to \[=4\int_{0}^{1}{|\log x|dx=-4\int_{0}^{1}{\log x\,\,dx}}\], (\[\because \]In