Chapter 3: Integration

3.1: Introduction

1. Antidifferentiation and Indefinite Integral
2. Differentials of Variables
3. Integral Language and Notation
4. Difference between Delta y and dy
5. Problem1-Difference between Delta y and dy

3.2: Integration as Anti-Derivative

1. Theorems on Anti-derivative
2. Problem1-Theorems on Anti-derivative
3. Problem2-Theorems on Anti-derivative
4. Problem3-Theorems on Anti-derivative
5. Problem4-Theorems on Anti-derivative
6. To Integrate x Raise to Power n
7. Problem1-To Integrate x Raise to Power n
8. To Integrate Sine Functions
9. To Integrate Cosine Functions
10. To Integrate Secant Squared Fucntions
11. To Integrate secx.tanx
12. To Integrate Cosecant.Cotangent Functions
13. Integrating Exponential Functions
14. To Integrate 1 by x
15. To Integrate Tangent Functions
16. To Integrate Cotangent Functions
17. To Integrate Cosecant Functions
18. Integrating Power Functions with Given Derivatives
19. More on Integrating Power Functions with Given Derivatives

3.3: Integration By Method of Substitution

1. Integration by Substitution

3.4: Some Useful Substitutions

1. Some Useful Substitutions in Integration
2. More on Some Useful Substitions in Integration
3. Some More Useful Substitions in Integration
4. Problem-Integration by Useful Substitution
5. Problem2-Some More Useful Substitions in Integration
6. Prolem3-Some More Useful Substitions in Integration
7. Prolem4-Some More Useful Substitions in Integration
8. Prolem5-Some More Useful Substitions in Integration

3.5: Integration By Parts

1. Integration by Parts
2. More on Integration by Parts
3. Problem1-Integration by Parts
4. Problem2-Integration by Parts
5. Problem2b-Integration by Parts
6. Integration by Parts of Trigonometric Functions
7. More on Integration by Parts of Trigonometric Functions

3.6: Integration Involving Partial Fractions

1. Integrating Partial Fractions with Non-repeated Factors
2. Problem1-Integrating Partial Fractions with Non-repeated Factors
3. Problem1a-Integrating Partial Fractions with Non-repeated Factors
4. More on Integrating Partial Fractions with Non-repeated Factors
5. Integrating Partial Fractions with Non-repeated Linear Factors
6. Problem1-Integrating Partial Fractions with Non-repeated Linear Facto
7. Problem1a-Integrating Partial Fractions with Non-repeated Linear Fact
8. More on Integrating Partial Fractions with Non-repeated Factors
9. Integrating Partial Fractions with Non-Repeated Quadratic Factors
10. Problem1-Integrating Partial Fractions with Non-Repeated Quadratic Fa
11. Problem1a-Integrating Partial Fractions with Non-Repeated Quadratic F
12. More on Integrating Partial Fractions with Non-Repeated Quadratic Fac
13. Further to Integrating Partial Fractions with Non-Repeated Quadratic

3.7: The Definite Integrals

1. The Definite Integral
2. Problem1-The Definite Integral
3. Problem2-The Definite Integral
4. Problem2a-The Definite Integral
5. Area Under the Curve
6. Problem1-Area Under the Curve
7. Problem2-Area Under the Curve
8. More on Area Under the Curve
9. Negative Area by Definite Integral
10. Symmetrical Area by Integration
11. Area Bounded by Two Curves by Integration
12. To Deal with Negative and Positive Areas in Integation
13. Area Bounded by Two Curves Above and Below x-axis

3.8: Applications of Definite Integrals

1. Application of Definite Integral
2. More on Application of Definite Integral
3. Problem1-Application of Definite Integral
4. Problem2-Application of Definite Integral
5. Problem2a-Application of Definite Integral
6. Problem3-Application of Definite Integral
7. Problem3a-Application of Definite Integral

3.9: Differential Equations

1. Introduction to Differential Equation
2. More on Introduction to Differential Equation
3. Classification of Differential Equation
4. More on Classification of Differnetial Equation
5. Solving First Order Differential Equation
6. More on Solving First Order Differential Equation
7. Problem1-Solving First Order Differential Equation
8. Problem2-Solving First Order Differential Equation
9. Solving First Order Differential Equation by Initial Conditions
10. P1-Solving First Order Differential Equation by Initial Conditions
11. P2-Solving First Order Differential Equation by Initial Conditions
12. P3-Solving First Order Differential Equation by Initial Conditions
13. Homogeneous Differential Equation
14. Differential Equation Reducible to Homogeneous Differential Equation
15. Differential Equation of Orthogonal Trajectories
16. More on Differential Equation of Orthogonal Trajectories
17. Application of Differential Equations
18. More on Application of Differential Equations