Deriving the Work Done by an Inverse Square Force in Non-Calculus-Based Introductory Physics Courses

Abstract

I describe a method of evaluating the integral of 1/2r² with respect to r that uses only algebra and the concept of area underneath a curve, and which does not formally employ any calculus. This is useful for algebra-based introductory physics classes (where the use of calculus is forbidden) to derive the work done by the force of one point charge or mass on another. I extend the method to evaluate any integral of the form ∫rn dr for any integer n ≠ −1.