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Math Help - More polar help needed

  1. #1
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    More polar help needed

    Find the area between the curves r=sin(theta) and r=2sin(theta).

    Find the area of the region enclosed by r=3cos3(theta)
    Last edited by leinadwerdna; April 28th 2009 at 02:34 PM. Reason: forgot something
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  2. #2
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    Quote Originally Posted by leinadwerdna View Post
    Find the area between the curves r=sin(theta) and r=2sin(theta).
    make a sketch?

    geometric method ...

    A = area of big circle - area of little circle = \frac{3\pi}{4}

    calculus method ...

    2 \int_0^{\frac{\pi}{2}} \frac{1}{2}(2\sin{\theta})^2 - \frac{1}{2}(\sin{\theta})^2 \, d\theta

    \int_0^{\frac{\pi}{2}} 3\sin^2{\theta} \, d\theta


    Find the area of the region enclosed by r=3cos3(theta)
    6\int_0^{\frac{\pi}{6}} \frac{1}{2}[3\cos(3\theta)]^2 \, d\theta
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