# Thread: Area of a Polar Curve

1. ## Area of a Polar Curve

Question asks: what is the area between the large petals and small petals for the curve $\displaystyle r=1+2sin3\theta$

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

$\displaystyle 2\int_{\frac{\pi}{6}}^{\frac{7\pi}{18}} \frac{r^2}{2} \, d\theta$

small petal ...

$\displaystyle 2\int_{\frac{7\pi}{18}}^{\frac{\pi}{2}} \frac{r^2}{2} \, d\theta$

3. Originally Posted by skeeter
large petal area ...

$\displaystyle 2\int_{\frac{\pi}{6}}^{\frac{7\pi}{18}} \frac{r^2}{2} \, d\theta$

small petal ...

$\displaystyle 2\int_{\frac{7\pi}{18}}^{\frac{\pi}{2}} \frac{r^2}{2} \, d\theta$
Would you mind explaining how you obtained those limits on your integrals?

4. Originally Posted by Em Yeu Anh
Would you mind explaining how you obtained those limits on your integrals?
started by looking for values of $\displaystyle \theta$ 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.