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Tests for Improper Integrals

Tests for Improper Integrals
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2026-09-26 07:09
CalculusIntegralLimit
This GeoGebra example demonstrates how to test improper integrals. It shows how to use various convergence tests to determine whether an integral converges or diverges. Key mathematical concepts include convergence tests, convergence and divergence of integrals. Construction points include using the CurveCartesian command to plot function graphs, and using the Integral command to compute integrals. Suitable for middle school and high school mathematics education, particularly for teaching calculus and integral calculus.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, f(t), t, 0, 100) → b
  2. CurveCartesian(t, 1 / t, t, 0, 100) → c
  3. Integral(1 / x, 1, 100) → d
  4. Integral(1 / x^(2), 1, 100) → e
  5. Integral(1 / x^(a), 1, Infinity) → i
  6. Integral(1 / x^(a), 1, 1000) → g

AI Drawing Prompt Reference

Create a single coordinate plane showing curves related to improper integrals. Plot the function graph y = 1/x over t from 0 to 100 as a main curve, alongside a generic function graph y = f(t) over the same t-range as a placeholder. Then include integral computations as reference results: evaluate ∫(1/x) dx from 1 to 100 and ∫(1/x^2) dx from 1 to 100. Also include the improper integral form ∫(1/x^a) dx from 1 to Infinity for a convergence/divergence test, and provide the finite upper-limit version ∫(1/x^a) dx from 1 to 1000 in parallel.
The prompt above was compiled from the original drawing commands and is for reference only.