Line integral

**asi123** · August 14th 2008, 07:39 AM

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?

**wingless** · August 14th 2008, 11:02 AM

$\vec{r} = \sin t \cos t \mathbf{i} + \sin^2 t \mathbf{j}$

$\vec{r} = \frac{\sin 2t}{2} \mathbf{i} + \frac{1-\cos 2t}{2} \mathbf{j}$

$\vec{r} = \frac{\sin 2t}{2} \mathbf{i} + \left ( \frac{1}{2}-\frac{\cos 2t}{2} \right ) \mathbf{j}$

It can be seen that this is a circle of radius $\tfrac{1}{2}$ centered at $(0,\tfrac{1}{2})$ . Note that the interval $0\leq t \leq 2\pi$ draws the circle twice.

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