Find Region Enclosed by Function r=2sin2θ

[aks_sky]

Find the region enclosed by one leaf of the function r=2 sin2θ


Now i know how the diagram looks like for this function.
The diagram can be obtained by using :

x= r cosθ = 2 sin2θ cosθ
y= r sinθ = 2 sin2θ sinθ

Now i have to find the region enclosed by one of the leaves which i am not able to do.
I know i have to use the jacobian and also that i can use the above as cylindrical coordinates but what do i integrate? i don't know which function to integrate.

Any Suggestions for that??

thank you

 

[rootX]

$$\frac{1}{2}\int r^{2} .d\theta$$

You can use that formula

 

[berkeman]

$$\frac{1}{2}\int r^{2} .d\theta$$

You can use that formula

Wouldn't it be $$\int r d\theta$$

I could be missing something of course...

 

[aks_sky]

Is the half for finding each half of the region of the leaf?