Interactive resource
Riemann Sums: Approximating Area Under a Curve
Calculus. Interactive left, midpoint, and right Riemann sums — refine partitions to approach a definite integral.
Overview
A definite integral is net area under a curve. Riemann sums tile that area with rectangles; finer partitions usually get closer.
Explanation
The definite integral ∫ₐᵇ f(x) dx is the net area under y=f(x) on [a,b].
A Riemann sum splits the interval into n pieces and uses left, right, or midpoint sample heights.
For continuous f, larger n usually improves the approximation.
How to use
- Open the Riemann-sum scene.
- Switch left / mid / right endpoints.
- Increase the number of partitions n.
- Compare the sum with the exact integral readout.
Teaching tip
Keep the interval fixed and raise n from 4 to 20 so students watch the error shrink.
Knowledge points
FAQ
Must students know antiderivatives first?
Use this for geometric motivation; compute formulas afterward.
Is this tool free?
Yes. It runs in the browser with no install.
Good for class demos?
Yes — project it and ask what changes when you drag a parameter.
How do I write the formula afterward?
Open the equation editor or symbol sheet and copy a clean expression.