Question

The area bounded by the curve $y=x^2$ and $y=\frac{2}{1+x^2}$ is $\lambda sq.unit$, then the value of $\left[\lambda \right]$ is

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is A $2$

Required area = ${\int }_{-1}^1(\frac{2}{1+x^2}-x^2)dx$
$2{\int }_0^1(\frac{2}{1+x^2}-x^2)dx$
$2{(2ta{n}^{-1}x-\frac{x^3}{3})}_0^1=2(\frac{\pi }{2}-\frac{1}{3})=\pi -\frac{2}{3}$
$\therefore [\pi -,\frac{2}{3}]=2$