Question

The area bounded by curve $y=\ln x,x=1,x=2$ and x-axis is

• A. $\ln 4e$
• B. $\ln \frac{4}{e}$
• C. $\ln \frac{e}{4}$
• D. $\ln \frac{3}{e}$

Answer 1

The correct option is B $\ln \frac{4}{e}$

Area $:[y=lnx,x=2,x=1]$

$A={\int }_1^{2}1dnxdx$

$xlnx-\int x.\frac{1}{x}dx$

$=xlnx-\int x.\frac{1}{x}dx$

$=xlogx-x{|}_1^2$

$=x(logx-1){|}_1^2$

$=2(log2-1)-1(log1-1)$

$\Rightarrow 2ln2-ln1-2+1$

$\Rightarrow ln{2}^2-ln1-1$

$=ln4-lne....\left(0\right)$

$=ln\left(\frac{4}{e}\right),$ option B is correct