How to Accurately Calculate the Area Between Polar Curves Using Integrals
To find the area between polar curves, identify the region bounded by two curves, \( r = f(\theta) \) and \( r = g(\theta) \), over an interval \([ \alpha, \beta ]\). The area between these curves is calculated by integrating the difference in their radial values squared: \([\text{Area} = \frac{1}{2} \int_{\alpha}^{\beta} \left( f(\theta)^2 – […]