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Improper Integral of Power Functions

Improper Integral of Power Functions
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2018-03-06 08:51
FunctionCalculusIntegral
This example demonstrates how to use GeoGebra to plot the improper integral of power functions. The core math concepts involved include functions, power functions, integration, and limits. Key construction points involve using commands and objects such as Point, OrthogonalLine, Intersect, IntegralBetween, Line, Mirror, and Integral. Suitable for high school and above students to learn and understand the concept of integration in calculus.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. OrthogonalLine(A, xAxis) → g
  3. Intersect(f, g, (1, 1)) → B
  4. OrthogonalLine(C, yAxis) → h
  5. Intersect(f, h, (4.277348608069011, 0.012778387641685004)) → D
  6. Intersect(f, h, (4.277348608069011, 0.012778387641685004)) → E
  7. IntegralBetween(f, ((-(x(h) / y(h))) * x) - z(h) / y(h), x(B), x(E)) → a
  8. Line((0, 0), (1, 1)) → i
  9. Mirror(h, i) → h'
  10. Intersect(f, h', (0.01277838764953576, 479260.7061294759)) → F
  11. Integral(f, x(F), x(B)) → b