Area

The given curve is symmetric in the 4 quadrants. So, the required area is:

$\displaystyle \Rightarrow 4 \displaystyle \int_{0}^{1} \sqrt{x^2(1-x^2)} dx$

Substituting $x = \sin\theta \displaystyle \Rightarrow dx = \cos\theta d\theta$ :

$\displaystyle \Rightarrow 4 \displaystyle \int_{0}^{\frac{\pi}{2}} \sin\theta \cos^2\theta d\theta$

$\displaystyle \Rightarrow \frac{4}{3} = \boxed{1.333}$