Rectangular Sums: Approximating Area Under a Curve with Rectangles and Trapezoid

This interactive GeoGebra worksheet shows how the area under a curve can be approximated by summing rectangles (upper and lower Riemann sums) or trapezoids (trapezoidal rule). Users can move a slider to change the number of subintervals n and watch the approximation converge to the exact definite integral. The construction uses the GeoGebra commands RectangleSum and TrapezoidalSum, places points and text fields to label the interval endpoints a and b, displays the computed Riemann sum and trapezoidal sum, and compares them with the exact integral value. It is ideal for high‑school or early‑college calculus students learning about Riemann integration, the definition of the definite integral, and numerical integration techniques.