Question

The area of the region bounded by the curves $y=x^{3}, y=\frac{1}{x}, x=2$ is

• A. $4- \log_{e} 2$
• B. $\frac{1}{4}+ \log_{e} 2$
• C. $3- \log_{e} 2$
• D. $\frac{15}{4}- \log_{e}2$

Answer 1

Answer: (B)

$\frac{1}{4}+ \log_{e} 2$

Answer 2

First of all we draw the graph,
$y=x^{3}, y=\frac{1}{x}, x=2$

$\therefore$ Required area i.e., (OMPNO)
$=\int\limits_{0}^{1} x^{3} d x+\int\limits_{1}^{2} \frac{1}{x} d x$
$=\left[\frac{x^{4}}{4}\right]_{0}^{1}+\left[\log _{e} x\right]_{1}^{2}$
$=\frac{1}{4}+\log _{e} 2$