How to Find the Area Enclosed by Curves Using Any Axes
Finding the area between curves is a fundamental concept in integral calculus that involves computing the region enclosed by two or more functions over a specific interval. This is achieved by integrating the difference between the functions. The method depends on how the functions are defined: if they are functions of \( x \), use […]
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 – […]
