indefinite integral
Original function and indefinite integral
Provided the function f (x) is defined on a certain interval I, if present, can be derived function F (x), for any point on the interval has F '(x) = f ( x) established, called F (x) is f (x) in the interval I is a primary function
, Where C is an arbitrary constant
Original function (indefinite integral) existence theorem
- Continuous function f (x) must primitive F (x)
- Containing the first type of discontinuity point, the discontinuous point infinity function f (x) in including the discontinuity point within the interval will not have the original function F (x)
Definite integral
- If f (x) <0, below the curved side trapezoid in the x-axis, the definite integral of the absolute value remains equal to the area of the trapezoid curved edge , but the value of the integral is negative in
Definite integral precise definition (special form can be calculated limit of the number of columns)
Existence Theorem definite integral (definite integral is present, (usually sense) INTEGRABILITY known as functions of one variable)
Chang Yi, "limited range, bounded function"; abnormal "range is infinite, unbounded function"
Definite integral exists sufficient condition
Definite integral present requirement (bounded understood from the integral curve area can not be infinite)
Definite Integral Property
Seeking nature of a section length
Properties of the linear nature of integral 2
3 Properties of Integrals
Paul No. 4 integral nature of the
Below, the absolute value of the integral is 0, the absolute value of twice the integral of the pattern area
Number of Paul
Property valuation Theorem 5
6 properties (the integral theorem)
Continuous, there is provided at least on the f (x) in the closed interval [a, b] in the [a, b] the point [xi], such that 
Integral limit change
Nature becomes limited integration
