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Math Help - Polar Integration

  1. #1
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    Polar Integration

    I am given two functions: r=1-\sin\theta and r=0.5. I am asked to find the area inside the cardioid and outside of the circle. How should I proceed? Are there any good resources for these types of problems?

    Thanks,
    Peter
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  2. #2
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    Quote Originally Posted by flybynight View Post
    I am given two functions: r=1-\sin\theta and r=0.5. I am asked to find the area inside the cardioid and outside of the circle. How should I proceed? Are there any good resources for these types of problems?

    Thanks,
    Peter
    note the cardiod and circle intersect at \displaystyle \theta = \frac{\pi}{6} in quad I.

    using the symmetry of the y-axis ...

    \displaystyle A = 2 \int_{-\frac{\pi}{2}}^{\frac{\pi}{6}} \frac{(1-\sin{\theta})^2}{2} - \frac{1}{8} \, d\theta
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