Question

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

Answer 1

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

Area of the shaded region $=$ area of $OAD$+area of $ABCD$

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

$=\frac{1}{2}\times 1\times 1+[\ln x{]}_1^e$

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

$=\frac{1}{2}+1+0=\frac{3}{2}$ units