question_answer

The area bounded by the curves \[x={{y}^{2}}\] and \[x=\frac{2}{1+{{y}^{2}}}\] is

A) \[\pi -\frac{2}{3}\]

B) \[\pi +\frac{2}{3}\]

C) \[-\pi -\frac{2}{3}\]        

D) none of these

Correct Answer: A

Solution :

[a] Solving curves, we get point of intersection \[(1,\pm 1).\] Required area is \[2\int_{0}^{1}{\left( \frac{2}{1+{{y}^{2}}}-{{y}^{2}} \right)dy=\pi -\frac{2}{3}}\]