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Math Help - polar coordinate

  1. #1
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    polar coordinate

    Find the area of the region inside: r = 8 \sin \theta but outside  r = 4
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  2. #2
    Senior Member tukeywilliams's Avatar
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    First find the points of intersection.

    So  8 \sin \theta = 4, \ \sin \theta = \frac{1}{2} or  \theta = \frac{\pi}{6}, \ \frac{5 \pi}{6} .

    So  A = \frac{1}{2} \int_{\frac{\pi}{6}}^{\frac{5 \pi}{6}} (8 \sin \theta)^2 \ d \theta - \frac{1}{2} \int_{\frac{\pi}{6}}^{\frac{5 \pi}{6}} 16 \ d \theta .
    Last edited by tukeywilliams; July 24th 2007 at 02:45 PM.
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  3. #3
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    how did you get 81 in the 2nd integral?
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  4. #4
    Senior Member tukeywilliams's Avatar
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    it should be  16 .
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  5. #5
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    Quote Originally Posted by viet View Post
    Find the area of the region inside: r = 8 \sin \theta but outside  r = 4

    Maple-generated graph

    plot([8*sin(theta),4],theta=0..2*Pi,coords=polar,thickness=3,color=[red,blue]);
    Attached Thumbnails Attached Thumbnails polar coordinate-july23.gif  
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