1. If f(x) is an even function, then? This is the so-called heiji.
The definite integral of the interval [-a, a] in which even functions are symmetrical about the origin is twice that of the interval [0, a].
2. If f(x) is odd function, then? This is called odd zero.
The definite integral of odd function interval [-a, a] with symmetric origin is 0.
Together, they are called parity zero.
Extended data:
Parity zero is an important calculation property of double integral and triple integral, as follows
Let the function f(x, y) be continuous on the bounded closed region d:
1. If d is symmetric about x and the area above the x axis is D 1, then there is
2. If D is symmetrical about Y axis and the area on the right side of Y axis is D 1, then there is
3. If the integration region d is symmetrical about the origin, double integration is performed.
Where D 1 is the upper half of d.
The above is the calculation property of "even times odd zero". Note that when used, the symmetry of the integral region should match the parity of the integrand function. That is, the integral region is symmetrical about x, and the integrand has parity about y variable; The integration region is symmetric about Y axis, and the integrand has parity about X variable, so the integration is even times odd zero.