# Math Help - Area of Rose Leaf - Polar Coordinates

1. ## Area of Rose Leaf - Polar Coordinates

Find the area inside one leaf of the rose:

r = 4 sin(5θ)

2. ## Area of Polar Curve

**post editted - deleted**

3. Originally Posted by Del
Find the area inside one leaf of the rose:

r = 4 sin(5θ)

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