Area Between Curves with Riemann Sums

Area Between Curves with Riemann Sums
Loading the math board and drawing, please wait…
2017-02-07 13:04
① This GeoGebra example visualizes the area enclosed between two function curves using dynamic Riemann sums, updating the approximate area as parameters change. ② Core mathematical concepts include definite integrals, Riemann sums, area between curves, and the limiting process where finer partitions yield more accurate approximations. ③ Construction details: uses Function to define f and g, Segment to partition the interval, Sequence to generate rectangles, and IntegralBetween to compute the exact area; sliders a, b control the integration interval, slider n controls the number of subintervals, with lists list1 and list2 storing rectangle vertices and text objects displaying values. ④ Ideal for high school or early college calculus students to grasp the geometric meaning of integration and numerical approximation, and for teachers as an interactive demonstration tool.

GeoGebra Commands & Parameters

  1. Function((x - 1)^(3) - (2 * (x - 1)^(2)) + 2, -20, 20) → f
  2. Function(cos(x), -20, 20) → g
  3. Segment((a, -0.1), (a, 0.1)) → h
  4. Segment((b, -0.1), (b, 0.1)) → i
  5. Sequence(a + (i * (b - a) / n), i, 0, n - 1, 1) → list1
  6. IntegralBetween(f, g, a, b) → d
  7. Sequence(Polygon[(Element[list1, i], g(Element[list1, i])), (Element[list1, i] + (b - a) / n, g(Element[list1, i])), (Element[list1, i] + (b - a) / n, f(Element[list1, i])), (Element[list1, i], f(Element[list1, i]))], i, 1, n, 1) → list2

AI Drawing Prompt Reference

Visualize the area enclosed between two function curves using dynamic Riemann sums, updating the approximate area as parameters change. Partition the interval with line segments, generate rectangles using a sequence, and compute the exact area. Sliders control the integration interval and number of subintervals, with lists storing rectangle vertices and text objects displaying values.
The prompt above was compiled from the original drawing commands and is for reference only.