# Area between two polar curves

1. Jan 9, 2010

### Charismaztex

1. The problem statement, all variables and given/known data

Find the area between the two curves:

$$r=2sin(\theta), r=2(1-sin(\theta))$$

2. Relevant equations

$$A=\frac{1}{2} \int_{\beta}^{\alpha} r^2 d\theta$$

3. The attempt at a solution

I've got the points of intersection at $$(1,\frac{1}{6}\pi) and (1,\frac{5}{6}\pi)$$ and worked out the answer to be $$\frac{8}{3}-4\sqrt{3}$$ using the angles in the above polar co-ordinates as the limits, however my textbook says that the answer is $$\frac{7}{3}-4\sqrt{3}$$ Is anyone able to confirm which is the correct answer.

Charismaztex

2. Jan 9, 2010

### payumooli

2sin(t) is a circle
next is a kind of cycloidal
this is the formula i used in matlab
int((2*sin(t))^2,0,pi/6)+int((2-2*sin(t))^2,pi/6,pi/2)
gives area of one lobe
multiply by 2 for both the lobes

Last edited: Jan 9, 2010
3. Jan 9, 2010