Find The Area Bounded by the following curves
$\displaystyle x=a(\theta - \sin \theta $)
$\displaystyle y=a(1-\cos \theta $
$\displaystyle 0 \leqslant \theta \leqslant 2\pi $
THE LATEX IS AWESOME IN MHF NOW!!!
Well, I would first like to point out that what you have written aren't curves but just one curve defined parametrically. It's called a cycloid.
Anyway, I guess you'd like the area between it and the x-axis.
Just take the integral as always, but rewrite with theta:
$\displaystyle \int^{2a\pi}_0 y\,dx=\int^{2\pi}_0 a(1-\cos \theta)\,d(a(t-\sin \theta))=\int^{2\pi}_0 a^2(1-\cos \theta)(1-\cos \theta)\,dt$
$\displaystyle =\int^{2\pi}_0 a^2 (1-\cos \theta)^2\,dt$
Now you can solve this any way you like.