Why you use even and odd function in mathematics?

If you know that a function is even (or odd), it may simplify the analysis of the function, for several purposes. One example is the calculation of definite integrals: for an odd function, the integral of a function from (-x) to (x) (note 1) is zero; for an even function, this integral is twice the integral of the function from (0) to (x).

Note 1: That is, the area under the function; for negative values, this "area" is taken as negative) is