Area bounded by the curve $y=log x,$ x-axis , x=1 and x=2 in square units is :
Answer & explanation
Correct answer: option 2
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 $\int uv\,dx=\int u\int v\,dx-\int u'\int v\,dx\,dx$
$=[x\log x-x]_1^2$
$=2\log 2-2+1$
$=\log 4-\log e⇒\log (\frac{4}{e})$