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

1. Oct 27, 2008

### demersal

1. The problem statement, all variables and given/known data
Find the area of the region enclosed by the asteroid:
x=a*cos$$^{3}$$$$\theta$$
y=a*sin$$^{3}$$$$\theta$$

2. Relevant equations
A = $$\int$$$$\sqrt{\frac{dy}{d\theta}^{2}}+\frac{dx}{d\theta}^{2}$$

3. 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!

2. Oct 27, 2008

### rock.freak667

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