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For Educators · Riemann Sums

Riemann Sums for a curve fit

Built for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs. Simulate a curve fit live below — adjust the inputs and watch it respond, right in your browser.

Riemann SumsLive

approximating the definite integral

Controls

f(x)

Rectangles approximate the area under the curve. Add more and the Riemann sum converges to the true integral.

Presets

Rectangles

▶ Run in Python

Data Inspector

Riemann sum20.7111

Exact integral20.8000

Error0.0889

Governing equation

\int_{- 4}^{4} f (x) d x \approx i = 0 \sum 11 f (x_{i}) Δ x = 20.711, Δ x = 0.667 (midpoint)

Reading this result: With n=12 midpoint rectangles the step is dx = 0.667. The midpoint rule already cancels much of the error at each rectangle. Adding subintervals shrinks the error toward the exact integral; midpoint and trapezoid rules converge fastest (error ~1/n²), so from n=12 the estimate tightens quickly as you push toward n=100.

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Frequently asked questions

Is this good for educators?: Yes — this version of "Riemann Sums for a curve fit" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.