Q. The area bounded by $y = \log{x,\ \ x}$-axis and ordinates $x = 1,\ x = 2$ is
A) $\frac{1}{2}(\log{2)}^{2}$
B) $\log{(2/e)}$
C) $\log{(4/e)}$
D) $\log 4$
Explanation
(c)
$Requred\ area = \int_{1}^{2}{\log{x\ \ dx}}$
$= \lbrack x\log{x - x\rbrack_{1}^{2} = 2\log{2 - 1}}$
$= \log{4 - \log{e = \log\left( \frac{4}{e} \right)}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.