Find the area bounded by the curves y = x2 and $y=\frac{2}{1+x^2}$.
Answer & explanation
Correct answer: option 3
Shaded Area = $2\int\limits_0^A(\frac{2}{1+x^2}-x^2)dx$
Solve $y=\frac{2}{1+x^2}$ and y = x2, A ≡ (1,1)
⇒ Shaded Area = $2\int\limits_0^1(\frac{2}{1+x^2}-x^2)dx=π-\frac{2}{3}$