Summary Comprehensive Treatise on Integration

Comprehensive Treatise on
Integration
Prepared for Class 12 and Early Engineering




Contents

1 Introduction to Integration 3


2 Basic Integration Formulas 3

2.1 Standard Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3


3 Techniques of Integration 4

3.1 Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.2 Integration by Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.3 Partial Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4


4 Solved Examples 4


5 Applications of Integration 5

5.1 1. Area under Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

5.2 2. Volume of Solid of Revolution . . . . . . . . . . . . . . . . . . . . . . . . 5

5.3 3. Physics Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

5.4 4. Economics Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

5.5 5. Engineering Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1

, Mathematics Integration Treatise


6 Advanced Topics (Engineering Level) 6

6.1 Improper Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

6.2 Multiple Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

6.3 Line Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

6.4 Beta and Gamma Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 6




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