Definite Integrals and Area
by Anonymous
Slice ever-thinner rectangles under a curve to close in on the true area, and see why regions below the axis count as negative.
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About this app
Definite Integrals and Area is an interactive calculus learning app that explains how area under a graph represents accumulated distance and how rectangle sums approach a curve’s true area. Explore left and right Riemann sums for y = x²/4, then investigate signed area for y = x − 2, where regions below the x-axis count negatively. Guided missions and adjustable controls make the ideas of limits, approximation, and definite integration visual and hands-on.
Use cases
- High school students learning definite integrals and signed area
- Teachers demonstrating Riemann sums and limits in class
- Learners reviewing the relationship between speed, time, and distance
- Practice with left sums, right sums, and endpoint changes
Features
- Adjust speed v and time t to see distance as rectangle area
- Increase the number of rectangles and compare left and right sums
- Visualize the curve y = x²/4 and the gap between an approximation and the true area
- Change endpoint T for the line y = x − 2
- Display positive area above the axis and negative area below it
- Complete guided missions across three interactive lessons