# Area of a Polar Curve

• Mar 13th 2010, 04:46 PM
Em Yeu Anh
Area of a Polar Curve
Question asks: what is the area between the large petals and small petals for the curve $r=1+2sin3\theta$
• Mar 13th 2010, 05:38 PM
skeeter
Quote:

Originally Posted by Em Yeu Anh
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
$

small petal ...

$2\int_{\frac{7\pi}{18}}^{\frac{\pi}{2}} \frac{r^2}{2} \, d\theta
$
• Mar 13th 2010, 06:18 PM
Em Yeu Anh
Quote:

Originally Posted by skeeter
large petal area ...

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

small petal ...

$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?
• Mar 14th 2010, 04:20 AM
skeeter
Quote:

Originally Posted by Em Yeu Anh
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.