[advanced mathematics] [5] definite integral and its application

1. The concept and properties of definite integral

1.1 The definition of definite integral

1.2 Definite integral theorem

1.3 Approximation of definite integral

1.3.1 Rectangular method

1.3.2 Trapezoidal method

1.3.3 Parabola method

1.4 The properties of definite integral

1.4.1 nature 1

1.4.2 nature 2

1.4.3 nature 3

1.4.4 nature 4

1.4.5 nature 5

1.4.6 inference 1

1.4.7 inference 2

1.4.8 nature 6 ( Mean value theorem of definite integral ）

2. The basic formula of calculus

2.1 Theorem 1

2.2 Theorem 2

2.3 Theorem 3 Newton - Leibniz formula （ The basic theorem of calculus ）

3. Substitution method and partial integration method of definite integral

3.1 The substitution method of definite integral

3.2 Periodic function

3.3 Partial integration of definite integral

4. Anomalous integral

4.1 Anomalous integral of infinite limit

4.2 Anomalous integrals of unbounded functions ( Flawed integral )

4.2.1 Defect point and defect integral

4.2.2 Definition

5. Convergence method of abnormal integral

6. The element method of definite integral

7. Application of definite integral in geometry

2.1 The area of a plane figure

2.2 Arc length of plane curve

2.3 Volume

8. The application of definite integral in Physics

3.1 The work done by a variable force along a straight line

3.2 water pressure

3.3 Gravity