# Homework Help: How do you find the limits of integration of polar curves?

1. Aug 25, 2010

### Soubriquet

Find the area of the region in the plane enclosed by the cardioid $$r = 4+4\sin{\theta}$$

The book explains that "Because r sweeps out the region as $${\theta}$$ goes from $$0$$ to $$2{\pi}$$, these are our limits of integration."

2. Aug 25, 2010

### gabbagabbahey

When working in Plane Polar coordinates, if you are talking about closed curves, then $\theta$ always goes from 0 to $2\pi$.

3. Aug 25, 2010

### Soubriquet

In another question, the limits change. How do I tell if the function is a closed curve?
The question is "Find the area inside the smaller loop of the limacon $$r = 1+2cos(\theta)$$."
The books gives the limits $$2(\pi)/3$$ to $$4(\pi)/3$$."

4. Aug 26, 2010