TITLE: Using Green's theorem to compute an area of a region
QUESTION [7 upvotes]: I want to use Green's theorem for computing the area of the region bounded by the $x$-axis and the arch of the cycloid:

$$ x = t- \sin (t),\;\;\; y = 1 - \cos (t),\;\; 0 \leq t \leq 2\pi $$

So basically, I know the radius of this cycloid is 1.
And to use Green's theorem, I will need to find $Q$ and $P$. 
$$\int_C P\,dx + Q\,dy =  \iint_D \left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right) dA$$

REPLY [3 votes]: Since you are asked to find the area which corresponds to $ \iint_D  dA,$ so you need to have the following condition
$$ \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}=1. $$