Properties of the Definite Integral: CIS.PDI Interactive Demo

Loading the math board and drawing, please wait…

2018-06-23 06:26

This GeoGebra example demonstrates properties of the definite integral, such as additivity over intervals and linearity, through an interactive visualization. Core mathematical concepts include the definition of the definite integral, the relationship between integral bounds and values, and geometric interpretation as area under a curve. The construction uses the Integral command to compute areas, Textfield and input boxes for dynamic function entry, and Point, Line, Vector, Segment objects to build supporting geometry. Suitable for high school calculus or introductory college calculus, it helps students grasp integral properties visually and interactively.

GeoGebra Commands & Parameters

Integral(P, a, c) → IPac
Integral(P, c, b) → IPcb
Integral(P, a, b) → IPab
Textfield(P) → inputBox1
Point(yAxis) → D
Point(yAxis) → E
Line(D, E) → Xaxis
Line(Ypt, Xaxis) → Yaxis
Vector(G, J) → u
Vector(I, F) → v
Vector(H, K) → w
Segment(F, K) → f
Segment(F, J) → h
Segment(I, H) → i
Segment(G, I) → j
Integral(αP, a, b) → IαPab
Line(M, Yaxis) → Y2axis
Vector(J, αs_a) → e
Vector(K, αs_b) → d
Segment(αs_a, αs_b) → g
Point(d) → N
Segment(J, K) → m
Segment(G, I) → n
Segment(G, H) → p
Textfield(Q) → InputBox1
Integral(Q, a, b) → IQab
Integral(P(x) + Q(x), a, b) → IPQab
Line(O, Xaxis) → q
Vector(G, SQa) → r
Vector(H, SQb) → s
Segment(SQb, SQa) → t
Vector(K, SPQb) → u_1
Vector(SQb, SPQb) → v_1
Vector(SQa, SPQa) → w_1
Segment(SPQb, SPQa) → f_1
Vector(SQb, SQb1) → a_1
Segment(SPQb, SQb1) → g_1
Segment(SQb1, SPQa) → h_1
Vector(J, SQb1) → b_1
Point(f_1) → R