Question

The area (in sq. units) bounded by the curves $y=x^2$ and $y=\frac{2}{1+x^2}$ is

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

Answer 1

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


Required area $=\underset{-1}{\overset{1}{\int }}(\frac{2}{1+x^2}-x^2)dx$
$=2\underset{0}{\overset{1}{\int }}(\frac{2}{1+x^2}-x^2)dx$
$=2{(2{\text{tan}}^{-1}x-\frac{x^3}{3})}_0^1$
$=2(\frac{\pi }{2}-\frac{1}{3})=\pi -\frac{2}{3}$