MathPlotAI Logo MathPlotAI

Definite Integral Function Addition

Definite Integral Function Addition
Loading the math board and drawing, please wait…
2020-05-10 09:14
FunctionCalculusIntegralGraphing
This GeoGebra example visually demonstrates the area-addition property of definite integrals when combining two functions. It illustrates how to compute the total area between curves over a given interval using integral splitting and segment marking. Core concepts include definite integration, function addition, area calculation, and the linearity of integrals. Construction uses GeoGebra commands such as Point, If, IntegralBetween, Integral, and Segment, along with dynamic text and dotted segment objects. Suitable for high school and early university calculus courses as a teaching aid for understanding integral geometry and function behavior.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Point(x = d) → F
  4. Point(x = d) → G
  5. If(upto < 3.5, 0, If[upto < 4.5, upto - 3.5, 1]) → t
  6. IntegralBetween((t * f(x)), g(x) + (t * f(x)), a, b) → intabove
  7. Integral((t * f(x)), a, b) → intbelow
  8. Integral(f, a, b) → intf
  9. Integral(g, a, b) → intg
  10. Integral(s, a, b) → ints
  11. Segment(A, B) → theint