Question

For $b>a>1,$ the area enclosed by the curve $y=\ln x,y-$axis and the straight lines $y=\ln a$ and $y=\ln b$ is

• A. $b-a$
• B. $b(\ln b-1)-a(\ln a-1)$
• C. $(b-a)\ln a$
• D. $\left(\ln b\right)\left(\ln a\right)$

Answer 1

The correct option is A $b-a$


Given $y=\ln x$
$\Rightarrow x=e^y$
Required area is
$=\underset{\ln a}{\overset{\ln b}{\int }}{e}^{y}dy=[e^y{]}_{\ln a}^{\ln b}=(b-a)$