Question bank/JEE Main/Mathematics

Area bounded by $y = x^{2}\ and\ y = \frac{2}{1 + x^{2}}$ is.

A$\pi - \frac{1}{3}$B$\pi - \frac{2}{3}$C$2\pi - \frac{1}{3}$DNone of these

Show answer and solution▾

Clearly y = x^2 is a parabola
The curve $y = \frac{2}{1 + x^{2}}$ passes through; (0, 2) and as
$x \rightarrow \infty,y \rightarrow 0,$ Also y ≥ 2

[IMAGE] The points of intersection of these curves is given by
$x^{2} = \frac{2}{1 + x^{2}} \Rightarrow x^{4} + x^{2} - 2 = 0$
$\Rightarrow$ x^2 = -2,

Source: Grass-G / M-13 Mathematics Paper 4 Nov.docx