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