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

Answer 1

The correct option is B $\frac{3}{2}$ square units


Area of required region $AOCBA$
$=\underset{0}{\overset{1}{\int }}xdx+\underset{1}{\overset{e}{\int }}\frac{1}{x}dx={\left[\frac{x^2}{2}\right]}_0^1+{\left[\ln x\right]}_1^e$
$=\frac{1}{2}+1=\frac{3}{2}$ sq. units