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### 7. Integrals

• 7.1. Indefinite Integral
• 7.1.1. Antiderivative. Indefinite Integral and Its Properties
• 7.1.2. Table of Basic Integrals. Properties of the Indefinite Integral. Integration Examples
• 7.1.3. Integration of Rational Functions
• 7.1.4. Integration of Irrational Functions
• 7.1.5. Integration of Exponential and Trigonometric Functions
• 7.1.6. Integration of Polynomials Multiplied by Elementary Functions
• 7.2. Definite Integral
• 7.2.1. Basic Definitions. Classes of Integrable Functions. Geometrical Meaning of the Definite Integral
• 7.2.2. Properties of Definite Integrals and Useful Formulas
• 7.2.3. General Reduction Formulas for the Evaluation of Integrals
• 7.2.4. General Asymptotic Formulas for the Calculation of Integrals
• 7.2.5. Mean Value Theorems. Properties of Integrals in Terms of Inequalities. Arithmetic Mean and Geometric Mean of Functions
• 7.2.6. Geometric and Physical Applications of the Definite Integral
• 7.2.7. Improper Integrals with Infinite Integration Limit
• 7.2.8. General Reduction Formulas for the Calculation of Improper Integrals
• 7.2.9. General Asymptotic Formulas for the Calculation of Improper Integrals
• 7.2.10. Improper Integrals of Unbounded Functions
• 7.2.11. Cauchy-Type Singular Integrals
• 7.2.12. Stieltjes Integral
• 7.2.13. Square Integrable Functions
• 7.2.14. Approximate (Numerical) Methods for Computation of Definite Integrals
• 7.3. Double and Triple Integrals
• 7.3.1. Definition and Properties of the Double Integral
• 7.3.2. Computation of the Double Integral
• 7.3.3. Geometric and Physical Applications of the Double Integral
• 7.3.4. Definition and Properties of the Triple Integral
• 7.3.5. Computation of the Triple Integral. Some Applications. Iterated Integrals and Asymptotic Formulas
• 7.4. Line and Surface Integrals
• 7.4.1. Line Integrals of the First Kind
• 7.4.2. Line Integral of the Second Kind
• 7.4.3. Surface Integral of the First Kind
• 7.4.4. Surface Integral of the Second Kind
• 7.4.5. Integral Formulas of Vector Calculus
• References for Chapter 7

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