Question

The area included by the curve $y=\ln x,x-$axis and the two ordinates at $x=\frac{1}{e}$ and $x=e$ is

• A. $2-\frac{2}{e}$
• B. $1-\frac{1}{e}$
• C. $\frac{2}{e}$
• D. $\frac{1}{e}$

Answer 1

The correct option is A $2-\frac{2}{e}$


$A=\left|\underset{\frac{1}{e}}{\overset{1}{\int }}\ln xdx\right|+\underset{1}{\overset{e}{\int }}\ln xdx$$=\left|\right[x(\ln x-1){]}_{1/e}^1|+\left[x\right(\ln x-1){]}_1^e=2-\frac{2}{e}$