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[tex]^{3}[/tex][tex]\theta[/tex]
y=a*sin[tex]^{3}[/tex][tex]\theta[/tex]

Homework Equations

A = [tex]\int[/tex][tex]\sqrt{\frac{dy}{d\theta}^{2}}+\frac{dx}{d\theta}^{2}[/tex]

The Attempt at a Solution

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

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 [itex]cos^2\theta+sin^2\theta =1[/itex]