Solving for area using an integral (intro to parametric curves)

[demersal]

Homework Statement

Find the area of the region enclosed by the asteroid:
x=a*cos^{3}\theta
y=a*sin^{3}\theta

Homework Equations

A = \int\sqrt{\frac{dy}{d\theta}^{2}}+\frac{dx}{d\theta}^{2}

The Attempt at a Solution

\frac{dy}{d\theta} = 3asin^{2}\theta(cos\theta)
\frac{dx}{d\theta} = -3acos^{2}\theta(sin\theta)

Plugging that into the equation, I just cannot simplify this integral (sorry ... I tried to write it out but the code got beyond messed up!) from 0 to pi/2! I square them but cannot combine them. Is there an easy way to factor it? Any help you could offer would be greatly appreciated!

 

[rock.freak667]

Try the identity cos^2\theta+sin^2\theta =1