Question

The area(in $\text{sq.units}$) enclosed between the curve $y=x^2$ and $y=\frac{2}{1+x^2}$ is

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

Answer 1

The correct option is B $\pi -\frac{2}{3}$

The common region of the curve is shown in the figure :
Area $=2\underset{0}{\overset{1}{\int }}[\frac{2}{1+x^2}-x^2]dx$
$=2[\frac{\pi }{2}-\frac{1}{3}]=\pi -\frac{2}{3}$