Odd function's definite integral in symmetric interval is zero, and even function's definite integral in symmetric interval is twice as large as its half interval. This property is called parity zero for short.

Functional parity formula

Odd function odd function = odd function, even function+even function = even function, odd function× odd function = even function, even function× even function = even function, odd function× even function = odd function. The multiplication rule of the above parity function can be summarized as follows: the same even is different.

Function representation

1, analytical formula method

The method of expressing the functional relationship between two variables with an equation containing mathematical relationship is called analytical method. The advantage of this method is that it can express the quantitative relationship between function and independent variable concisely, accurately and clearly. The disadvantage is that it is often complicated to calculate the corresponding value, and some functional relationships in practical problems may not be expressed by expressions.

2. List method

The method of expressing the functional relationship between two variables by list method is called list method. The advantage of this method is that the corresponding function values can be read directly by knowing the values of the independent variables in the table; The disadvantage is that only some corresponding values can be listed and it is difficult to reflect the whole picture of the function.

3. Mirror image method

Take the values of the independent variable X and the corresponding dependent variable Y of a function as the abscissa and ordinate of a point respectively, and draw its corresponding point in the rectangular coordinate system. A graph composed of all these points is called an image of a function. This method of expressing functional relations is called image method. The advantage of this method is that the function relationship can be expressed visually through the function image; The disadvantage is that the quantitative relationship obtained from image observation is approximate.

4. Language narrative method

Describe the relationship between functions in language.