For K-12 Students · Riemann Sums
Riemann Sums for a matrix transform
Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a matrix transform live below — adjust the inputs and watch it respond, right in your browser.
Riemann SumsLive
approximating the definite integral
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Rectangles approximate the area under the curve. Add more and the Riemann sum converges to the true integral.
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Riemann sum20.7111
Exact integral20.8000
Error0.0889
Governing equation
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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- Is this good for k-12 students?
- Yes — this version of "Riemann Sums for a matrix transform" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
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- No. It runs in any modern browser, free, with no account required.