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Math Help - Area of Rose Leaf - Polar Coordinates

  1. #1
    Del
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    Area of Rose Leaf - Polar Coordinates

    Find the area inside one leaf of the rose:

    r = 4 sin(5θ)

    Please help!
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  2. #2
    Del
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    Area of Polar Curve

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  3. #3
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    Quote Originally Posted by Del View Post
    Find the area inside one leaf of the rose:

    r = 4 sin(5θ)

    Please help!
    the sine functin is equal to zero at points of the form \pi \cdot k \mbox{ where} k \in \mathbb{Z}

    so setting the argument equal to the above we get

    5 \theta = \pi \cdot k \iff \theta =\frac{\pi \cdot k}{5}

    so our limits of integration are k=0 and k=1 0 \mbox{and } \frac{\pi}{5}

    A=\frac{1}{2}\int_{0}^{\pi/5}(4\sin(5 \theta))^2 d\theta

    =8\int_{0}^{\pi/5}\sin^{2}(5\theta)d\theta

    I think you can get it from here.

    Good luck
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