Area bounded by the curve $y=log x,$ x-axis , x=1 and x=2 in square units is :

$log (\frac{4}{e})$

The correct answer is Option (2) → $\log (\frac{4}{e})$

$⇒\int\limits_1^2ydx$

$=\int\limits_1^2\log xdx$

$=[x\log x]_1^2-\int 1dx$

Using $\int uv\,dx=\int u\int v\,dx-\int u'\int v\,dx\,dx$

$=[x\log x-x]_1^2$

$=2\log 2-2+1$

$=\log 4-\log e⇒\log (\frac{4}{e})$