question_answer

Area of region bounded by \[x=0,y=0,x=2,y=2,y\le {{e}^{x}}\] and \[y\le ln\,x\]is

A)   \[6-4ln2\]        

B)  \[4ln2-2\]

C)  \[2\,ln2-4\]                   

D)  \[6-2ln2\]

Correct Answer: A

Solution :

            Required area \[=2\left[ 2-\int\limits_{1}^{2}{\ln \,x\,dx} \right]\,=6-4\ln \,2\]