Hey.
I need to use Green's theorem in order to solve this integral.
My question is, how can I find the area for the Green's theorem integral?
$\displaystyle \vec{r} = \sin t \cos t \mathbf{i} + \sin^2 t \mathbf{j}$
$\displaystyle \vec{r} = \frac{\sin 2t}{2} \mathbf{i} + \frac{1-\cos 2t}{2} \mathbf{j}$
$\displaystyle \vec{r} = \frac{\sin 2t}{2} \mathbf{i} + \left ( \frac{1}{2}-\frac{\cos 2t}{2} \right ) \mathbf{j}$
It can be seen that this is a circle of radius $\displaystyle \tfrac{1}{2}$ centered at $\displaystyle (0,\tfrac{1}{2})$. Note that the interval $\displaystyle 0\leq t \leq 2\pi$ draws the circle twice.