Riemann Sum & Area Under Curve Visualizer interactive tool
Enter function and interval
Riemann sum approximation
Approximate area under the curve on [0, 3] using 6 rectangles and a left Riemann sum:
≈ 6.8750
What Is Riemann Sum & Area Under Curve Visualizer?
A Riemann sum & area under curve visualizer approximates the integral of a function over an interval by drawing rectangles and summing their areas. It supports left, right, and midpoint Riemann sums.
Connecting Sums to Integrals
Early in calculus, the definite integral is defined as the limit of Riemann sums. This tool lets you see that process visually: increasing the number of rectangles n makes the approximation more accurate, and choosing different methods changes whether rectangles over- or under‑estimate the true area.
How To Use the Riemann Sum & Area Under Curve Visualizer
- Enter a function of x in the f(x) field using JavaScript/Math syntax (for example x*x or sin(x)).
- Set the interval [a, b] over which you want to approximate the area under the curve.
- Choose the number of rectangles n and select a method: left, right, or midpoint Riemann sum.
- The visualizer will draw rectangles under the curve and calculate the approximate area as their total area.
- Use the Example button to load a sample function and parameters, or Reset to clear everything.