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Math Help - Line integral

  1. #1
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    Line integral

    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?
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  2. #2
    Super Member wingless's Avatar
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    \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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