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Function Defined by Integral

Function Defined by Integral
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2014-08-31 18:45
FunctionCalculusIntegralGeometric ConstructionGraphing
This example demonstrates how the logarithmic function is defined by an integral. Key math concepts include integral, logarithmic function, and linear equations. GeoGebra commands used are Integral, Locus, OrthogonalLine, Intersect, and Segment. Suitable for high school mathematics education to understand the relationship between integral and function graphs.

GeoGebra Commands & Parameters

  1. Integral(f, 1, t) → F
  2. Locus(A, t) → lokus2
  3. OrthogonalLine(A, xAxis) → b
  4. Intersect(b, xAxis) → B
  5. Segment(A, B) → c
  6. Integral(f, 1, t_1) → a
  7. Locus(C, t_1) → loc1

AI Drawing Prompt Reference

Draw a graph demonstrating how the logarithmic function is defined by an integral. First, plot the logarithmic function curve, then show the integral process. Construct line segments using the intersection points of integral lines with the x-axis and draw the locus of these segments. Next, draw perpendicular lines from the intersection points to the x-axis and find their feet. Finally, plot line segments at the integral limits and show the locus of the upper limit to reveal the relationship between the integral and the function graph.
The prompt above was compiled from the original drawing commands and is for reference only.