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Math Help - Finding the area of a curve

  1. #1
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    Finding the area of a curve

    How do I find the area of the region in one loop of the curve that has polar equation r^2 = 3 cos^2(theta) - 9 sin^2(theta) ???
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  2. #2
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    Polar integration is \frac{1}{2}\int_{\alpha}^{\beta}[f({\theta})]^{2}d{\theta}=\frac{1}{2}\int_{\alpha}^{\beta}r^{2  }d{\theta}

    You already have r^2.

    The area of half a loop in the first quadrant is \frac{1}{2}\int_{0}^{\frac{\pi}{6}}\left[3cos^{2}{\theta}-9sin^{2}{\theta}\right]d{\theta}

    Integrate and multiply by 2.
    Last edited by galactus; November 24th 2008 at 06:38 AM.
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