How do I divide the radius into subsections?
In one situation the region can be inside two circles and $\Delta r$ might equal for instance $\dfrac{2 - 1}{n}$. With another two radii that keep the variable in that format, like $\Delta r = \dfrac{cos(2\theta) - cos(\theta)}{n}$ how do you calculate the $\Delta r$ that's uniform everywhere? If I pick a sample of $\theta$ then I get uniform sub regions yet that seems like it should change the boundaries of integration. If the value of $\theta$ would vary then the regions don't have equal lengths of radius in the approximation. How do I always see this un evaluated expression as sub regions in the approximation walkthroughs?