question_answer

The area of the region enclosed by the curves \[y=x\], \[x=e,y=\frac{1}{x}\] and the positive x-axis is.   AIEEE  Solved  Paper-2011

A) \[\frac{5}{2}\] square units            

B) \[\frac{1}{2}\] square units

C) 1 square units      

D)  \[\frac{3}{2}\] square units

Correct Answer: D

Solution :

          Required area \[=\,\,\frac{1}{2}\times 1\times 1+\int\limits_{1}^{e}{\frac{1}{x}dx}\] \[=\frac{1}{2}+[Inx]_{1}^{e}\]  \[=\frac{1}{2}+1-0=\frac{3}{2}\] sq. units