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

• A

  $4-\log _{e} 2$
• Correct answer
  B

  $\frac{1}{4}+\log _{e} 2$
• C

  $3-\log _{e} 2$
• D

  $\frac{15}{4}-\log _{e} 2$

Solution

First of all we draw the graph $y=x^{3}, y=\frac{1}{x}, x=2$ Required area i.e., (OMPNO) $=\int_{0}^{1} x^{3} d x+\int_{1}^{2} \frac{1}{x} d x$ $=\left[\frac{x^{4}}{4}\right]_{0}+\left[\log _{4} x\right]_{1}^{2}=\frac{1}{4}+\log _{c} 2$

Hence, the correct answer is option: 'B'.