Start of the Integration Course from scratch for students and teachers. Course: Integration From Scratch General Objective: Guide the student from the basics to a solid mastery of indefinite and definite integrals, techniques, and applications. Module 1: Previous Foundations and Motivation Goals: Understand the concept of area under the curve as a motivation for the integral. Establish a basis with functions and derivatives. Contents: 1. What is integration? (visual intuition) 2. Review of functions (linear, quadratic, exponential) 3. Derivative and its relationship with the integral 4. Introduction to the integration symbol Exercises: Identify areas under simple curves (visually). Relate known derivatives with antiderivatives. Module 2: Indefinite Integrals Goals: Learn to calculate antiderivatives of common functions. Contents: 1. Definition of indefinite integral 2. Integration rules: Constant Powers Addition/subtraction 3. Integration by substitution 4. Integration by parts (simple introduction) Exercises: 15 graded exercises with feedback. Module 3: Definite Integrals and Fundamental Theorem Goals: Calculate exact areas under curves using definite integrals. Understand and apply the fundamental theorem of calculus. Contents: 1. Definition of definite integral 2. Geometric interpretation 3. Properties (linearity, additivity) 4. Fundamental Theorem of Calculus Exercises: 10 visual exercises + 10 algebraic exercises. Module 4: Integration Techniques Goals: Use advanced techniques to integrate more complex functions. Contents: 1. Trigonometric substitution 2. Partial fractions 3. Integration by parts (formal) 4. Numerical methods: trapezoidal rule Exercises: 20 problems per technique, with guided solutions and free practice. Module 5: Applications Goals: Apply integration to real-world problems. Contents: 1. Calculation of areas between curves 2. Volume of solids of revolution 3. Work and energy 4. Physical and economic problems Exercises: 10 practical problems with real-life context. Module 6: Evaluation and Final Challenges Goals: Measure learning and reinforce skills. Contents: 1. Final multiple-choice exam and development 2. Level-based challenges 3. Corrections in video or PDF Additional resources: Formula notebook Bank of integrals Explanatory videos Downloadable PDFs with theory and exercises

I'm Miguel Ángel, a Master of Science in Mathematics with extensive teaching experience. I provide personalized tutoring and tutoring classes in Mathematics and Physics, both online and in-person, tailored to any academic level. I specialize in helping students understand everything from basic to advanced topics with clear explanations, ongoing support, and strategies that actually work. What do I offer? 100% personalized advice Support with homework, exams, and projects Preparation for midterms and finals Practical and theoretical classes I work with all academic levels: secondary, pre-university, university, and graduate. Subjects I cover Basic Mathematics and Geometry Differential and Integral Calculus Linear and Nonlinear Algebra Series and Differential Equations Complex Variable Numerical Mathematics Probabilities and Statistics Laplace, Fourier and Z transforms Physics I, II and III

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