Interactive Mean Value Theorem for Integrals UNAD-ECBTI

Interactive MVT script for engineering students. Validates manual calculations with symbolic engine & auto-plotting. UNAD-ECBTI.

INTERACTIVE MEAN VALUE THEOREM FOR INTEGRALS Heutagogical Validation Script for Engineering Calculus | UNAD-ECBTI

OVERVIEW

This interactive MATLAB script supports engineering students in validating the Mean Value Theorem for Integrals through a self-determined learning approach. Developed for the Universidad Nacional Abierta y a Distancia (UNAD), School of Basic Sciences, Technology and Engineering (ECBTI), it bridges manual analytical calculation with symbolic computational validation.

Key Innovation: Students input their manual calculations first (f_prom, c, f(c)), then receive immediate feedback comparing their results against MATLAB's symbolic engine.

KEY FEATURES

• Heutagogical Validation Flow

• Students compute f_prom = (1/(b-a))∫[a,b] f(x)dx, c, and f(c) manually
• Script compares inputs against symbolic engine (vpasolve, int)
• Relative error calculation with adaptive feedback (<0.5% = Correct, ≥0.5% = Review + hints)

• Dynamic Personalization

• Function f(x) and interval [a,b] auto-assigned via η = mod(documento,10)
• 10 unique engineering contexts: signal decay, thermal profiles, wave propagation, pressure systems, etc.
• Prevents answer-sharing; ensures individual accountability

• Professional Visualization

• Publication-quality figure: f(x), horizontal line f_prom, point (c, f_prom)
• Shaded area under curve for geometric interpretation
• UNAD-branded colors and IEEE-style labels

• Traceability and Academic Integrity

• Unique 8-character verification code (hex) generated per execution
• Formatted output block ready to copy into Word reports
• Full screenshot requirement for evidence

• Symbolic and Numeric Hybrid Computation

• Symbolic integration (int) for exact f_prom
• Numerical fallback (linspace, min) if vpasolve fails
• Tolerance-controlled validation (1e-4 relative error threshold)

EDUCATIONAL CONTEXT

Course: Cálculo Integral (100411) Program: Ciencias Básicas, ECBTI, UNAD (Colombia) Pedagogical Model: MHUS 5.0 (Heutagogical Unadista Solidario) Competency Focus: Modeling, simulation, and data analysis (PEECBTI, Cap. 8) ODS Alignment: Quality Education (4), Industry/Innovation (9)

REQUIREMENTS

• MATLAB R2022b or newer (fully compatible with MATLAB Online) • Symbolic Math Toolbox (for int, vpasolve, symbolic expressions) • Internet connection for institutional license validation

HOW TO USE

1. Download Reto4_TeoremaValorMedio.m and open in MATLAB Online
2. Enter your full name and document number (η auto-calculated)
3. Review your assigned function f(x) and interval [a,b]
4. Compute manually first: f_prom, c, f(c) on paper/digital notebook
5. Input your manual results when prompted by the script
6. Review validation feedback, error analysis, and generated figure
7. Copy the formatted results block into your Word report
8. Export the figure (PNG ≥150 dpi) and include verification code

EXAMPLE OUTPUT

Estudiante : Juan Pérez Documento : 12345678 η : 8 Función : f(x) = (x-8)^3/8+2 Intervalo : [8.00, 16.00]

f_prom : 18.000000 c : 13.039684 f(c) : 18.000000 Estado : APROBADO Código Verif: 31F2BA20

TECHNICAL DETAILS

Symbolic Computation: syms x; f_prom = int(f(x), x, a, b) / (b - a); c_val = vpasolve(f(x) == f_prom, x, [a, b]);

Validation Logic: error_rel = abs(user_value - matlab_value) / matlab_value * 100; if error_rel < 0.5 disp('Correct!'); else disp('Review your procedure'); end

CITATION

If you use this script for educational or research purposes, please cite as:

González, J. F., and UNAD-ECBTI Team. (2026). Interactive Mean Value Theorem for Integrals: Heutagogical Validation Script for Engineering Calculus. MATLAB Central File Exchange. https://www.mathworks.com/matlabcentral/fileexchange/XXXXX

LICENSE

Released under BSD 3-Clause License for educational use, modification, and redistribution with attribution. Commercial use requires prior authorization from UNAD-ECBTI.

SUPPORT AND FEEDBACK

Technical issues or suggestions: [e-mail] Institutional inquiries: [e-mail] Course resources: Campus Virtual UNAD → Cálculo Integral (100411)

"MÁS UNAD, MÁS EQUIDAD" Red de Tutores Cálculo Integral, ECBTI, UNAD