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Math Help - Area of a Polar Curve

  1. #1
    Member Em Yeu Anh's Avatar
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    Question Area of a Polar Curve

    Question asks: what is the area between the large petals and small petals for the curve r=1+2sin3\theta
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  2. #2
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    Quote Originally Posted by Em Yeu Anh View Post
    Question asks: what is the area between the large petals and small petals for the curve r=1+2sin3\theta
    large petal area ...

    2\int_{\frac{\pi}{6}}^{\frac{7\pi}{18}} \frac{r^2}{2} \, d\theta<br />

    small petal ...

    2\int_{\frac{7\pi}{18}}^{\frac{\pi}{2}} \frac{r^2}{2} \, d\theta<br />
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  3. #3
    Member Em Yeu Anh's Avatar
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    Quote Originally Posted by skeeter View Post
    large petal area ...

    2\int_{\frac{\pi}{6}}^{\frac{7\pi}{18}} \frac{r^2}{2} \, d\theta<br />

    small petal ...

    2\int_{\frac{7\pi}{18}}^{\frac{\pi}{2}} \frac{r^2}{2} \, d\theta<br />
    Would you mind explaining how you obtained those limits on your integrals?
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  4. #4
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    Quote Originally Posted by Em Yeu Anh View Post
    Would you mind explaining how you obtained those limits on your integrals?
    started by looking for values of \theta that made r = 3 (tip of a large petal) and r = 0 (petal base).

    stumbled onto the value of r = -1 for the tip of the small petal during plotting.

    yes, some of us older folks remember how to plot polar graphs by hand.
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