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MATHEMATICS MISSIONS / CHALLENGE 11

Area Under Curve Explorer

Approximate area with Riemann sums and observe convergence toward a definite integral.

YOUR MATH BADGES0 / 12Problem solver
INTEGRAL BUILDERManipulate. Predict. Prove it visually.+1 MATH BADGE
LIVE MATHEMATICAL MODELREADY
10 left rectanglessum 7.6950 · exact 9.0000absolute error 1.3050
Riemann sum7.6950
Exact integral9.0000
Absolute error1.3050
Error meter
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The graph uses equal coordinate scale where geometry requires it. Values update directly from the displayed equations.
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Free online Riemann sum simulator

Area Under Curve Explorer: experiment guide

This browser-based simulation helps you approximate area with Riemann sums and observe convergence toward a definite integral. Designed for Grades 7–12, it turns an abstract idea into a model you can control, measure, reset, and test without signing up.

What you can investigate

Explore Riemann sums, definite integral, rectangles, area by changing the available controls and comparing the model’s visual and numerical evidence. Try one variable at a time, then combine changes to test a stronger explanation.

Riemann sumsdefinite integralrectanglesarea

How to use this simulation

  1. 1Read the mission and make a prediction before moving a control.
  2. 2Change one variable so its effect is easier to identify.
  3. 3Run the model and record a value, pattern, or visible change.
  4. 4Reset, test a different setup, and explain the result from evidence.

For students, teachers, and independent study

A typical investigation takes 8–15 min. Use it as a lesson demonstration, a guided inquiry activity, a homework experiment, or a quick review. The simulation runs in a modern web browser and does not require an account.

Level
Advanced
Time
8–15 min
Format
Simulation

Common questions

What does the Area Under Curve Explorer teach?

Approximate area with Riemann sums and observe convergence toward a definite integral. The main ideas are Riemann sums, definite integral, rectangles, area.

Is the Area Under Curve Explorer free to use?

Yes. You can run the simulation online for free without creating an account.

How long does the activity take?

Most learners can complete one investigation in 8–15 min. You can repeat it to compare more variables or improve your explanation.