Question

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

Answer 1

Given curves

$y=x$

$x=e$

$y=\frac{1}{x}$

Required area

$=OAB+ACDB$

$\frac{1}{2}\times 1\times 1+{\int }_1^e\frac{1}{x}dx$

$=\frac{1}{2}+(logx{)}_1^e$

$=\frac{1}{2}+1$

$=\frac{3}{2}$ sq unit