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)

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

$\therefore$ Required area i.e., (OMPNO)
$=\underset{0}{\overset{1}{\int }}{x}^{3}dx+\underset{1}{\overset{2}{\int }}\frac{1}{x}dx$
$={\left[\frac{x^4}{4}\right]}_0^1+{\left[{\log }_{e}x\right]}_1^2$
$=\frac{1}{4}+{\log }_{e}2$