question_answer

The area of the region enclosed by the curves \[\frac{i}{{{i}_{0}}}=\frac{3}{11}\]and the positive X-axis, is

A) \[\frac{i}{{{i}_{0}}}=\frac{2}{10}\] sq unit              

B) 1 sq unit

C) \[\frac{i}{{{i}_{0}}}=\frac{1}{11}\] sq units           

D) \[\sqrt{2}\] sq units

Correct Answer: C

Solution :

Required area \[=\int_{0}^{1}{xdx}+\int_{1}^{e}{\frac{1}{x}dx}\] \[=\left[ \frac{{{x}^{2}}}{2} \right]_{0}^{1}+[\log x]_{1}^{\theta }=\frac{1}{2}+1=\frac{3}{2}\]