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Graphical Animation of Average Value by Jason Slowbe

Graphical Animation of Average Value by Jason Slowbe
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2014-11-20 13:56
FunctionCalculusIntegralGraphing
In collections Average Value
This example demonstrates the graphical animation of the average y-value of a function over an interval. It involves core calculus concepts like integration, function graphs, and average value calculation. Constructed using GeoGebra commands such as Function, Integral, and Segment, along with objects like segments and text. Ideal for high school and above students studying calculus, function properties, and expected values in probability statistics.

GeoGebra Commands & Parameters

  1. Function(43.2, 0, 6) → h
  2. Function((x^(2) * (x - 6)^(2)), 0, 6) → f
  3. Function(((1 - a) * f(x)) + (a * h(x)), 0, 6) → g
  4. Integral(g, 0, 6) → k
  5. Segment(Q_2, J_1) → b
  6. Segment(P_2, I_1) → c
  7. Segment(O_2, H_1) → d
  8. Segment(N_2, G_1) → e
  9. Segment(M_2, F_1) → i
  10. Segment(K_2, D_1) → j
  11. Segment(J_2, C_1) → l
  12. Segment(I_2, B_1) → m
  13. Segment(H_2, A_1) → n
  14. Segment(L_2, E_1) → p
  15. Segment(G_2, Z) → q
  16. Segment(F_2, W) → r
  17. Segment(V_1, O) → s
  18. Segment(U_1, N) → t
  19. Segment(T_1, M) → a_1
  20. Segment(S_1, L) → b_1
  21. Segment(R_1, K) → c_1
  22. Segment(Q_1, J) → d_1
  23. Segment(P_1, I) → e_1
  24. Segment(O_1, H) → f_1
  25. Segment(V, E_2) → g_1
  26. Segment(D_2, U) → h_1
  27. Segment(T, C_2) → i_1
  28. Segment(B_2, S) → j_1
  29. Segment(R, A_2) → k_1
  30. Segment(Z_1, Q) → l_1
  31. Segment(P, W_1) → m_1
  32. Segment(N_1, G) → n_1
  33. Segment(F, M_1) → p_1
  34. Segment(L_1, E) → q_1
  35. Segment(A, K_1) → r_1

AI Drawing Prompt Reference

Draw a function graph showing the dynamic process of the average value over the interval [0, 6]. Start by plotting two base functions: one constant and one quadratic. Then, create a new function that is a weighted average of the base functions by adjusting a parameter dynamically. Next, compute the definite integral of the new function over [0, 6] to find the average value. Finally, use multiple line segments to connect key points on the function graph to the average value line, demonstrating the dynamic effect.
The prompt above was compiled from the original drawing commands and is for reference only.