Question

The area of the region enclosed by the curves $y=x,$ $x=e,y=\frac{1}{x}$ and the positive $x$ -axis is

• A. $\frac{5}{2}$ square units
• B. $\frac{1}{2}$ square units
• C. 1 square units
• D. $\frac{3}{2}$ square units

Answer 1

Answer: (D)

Required area
$=\frac{1}{2}\times 1\times 1+\underset{1}{\overset{e}{\int }}\frac{1}{x}dx$
$=\frac{1}{2}+[\ln x{]}_1^e$
$=\frac{1}{2}+1-0=\frac{3}{2}$ sq units