Calculating Areas of the Unit Hyperbola

Calculating Areas of the Unit Hyperbola
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2017-03-25 17:36
This example demonstrates how to calculate the area under the unit hyperbola using integration. Key math concepts include integral calculus, hyperbolas, and geometric constructions. It is constructed using GeoGebra commands like Textfield, Segment, Slope, IntegralBetween, Integral, If, and LaTeX, with objects such as InputBox1, t, P, O, V, h, r, m, h1, h2, APosRight, ALeft, ANegRight, A, text1. Ideal for high school students and calculus learners.

GeoGebra Commands & Parameters

  1. Textfield() → InputBox1
  2. Segment(O, P) → r
  3. Slope(r) → m
  4. IntegralBetween((m * x), h1, 1, x(P)) → APosRight
  5. Integral((m * x), 0, 1) → ALeft
  6. IntegralBetween(h2, (m * x), 1, x(P)) → ANegRight
  7. If(t ≥ 0, ALeft + APosRight, (-ALeft) + ANegRight) → A
  8. LaTeX(A, true, true) → text1