How to Use the Midpoint Riemann Sum
The midpoint Riemann sum is one of the most intuitive yet powerful tools in integral calculus for approximating the area under a curve. While left and right Riemann sums use the function's value at the edges of subintervals, the midpoint rule evaluates the function at the center of each subinterval. This subtle shift often yields a more accurate approximation, especially when the function is curved or nonlinear. Understanding how to apply the midpoint Riemann sum not only strengthens foundational calculus skills but also provides a practical method for numerical integration when an antiderivative is difficult or impossible to find.
At its core, a Riemann sum estimates the definite integral ∫ₐᵇ f(x) dx by dividing the interval [a, b] into n smaller subintervals, calculating the
