I'm having a difficult time applying the formula for areas under curves in polar form. My problem is deducing the limits of integration. For example, if I want to find the area of the interior for , I graph the function on my calc, and then I trace from the origin back to the y-axis. My calculator gives the angles in radians, which are and , so I can integrate to find the area.
What method can I use, in general, to find the limits of integration for problems like this? How can I determine on paper the interval through which the curve is traced?