Riemann Sum and Definite Integral Approximation

This applet demonstrates the concept of Riemann sums and their application in approximating definite integrals. Users can input custom functions and specify integration intervals, after which the system automatically adjusts the viewport display scale to fit the content. Through dynamically adjusting the number of subdivisions, the applet visually illustrates how the sum of rectangular areas progressively approaches the true area under the curve, providing an intuitive and engaging way to grasp the fundamental idea of integration and the limiting process in calculus. The interactive slider allows students to observe firsthand that as the number of rectangles increases, the approximation becomes increasingly accurate, converging toward the exact value of the definite integral. This hands-on exploration reinforces key mathematical concepts including partition, sample points, upper and lower sums, and the connection between finite summation and infinite limits, making abstract calculus principles more accessible and understandable for learners at all levels.