Teaching: the relationship between the value of double integral and the parity of integrand and the parity of integral region D Parity of integrand function with respect to X or Y What does it have to do with the value of the product? Compare this question: On the double integral of D: x ^ 2 * y DXDY D = {(x, y): x ^ 2 + y ^ 2 less than or equal to 2x} It is said that this double integral is equal to zero Why

Teaching: the relationship between the value of double integral and the parity of integrand and the parity of integral region D Parity of integrand function with respect to X or Y What does it have to do with the value of the product? Compare this question: On the double integral of D: x ^ 2 * y DXDY D = {(x, y): x ^ 2 + y ^ 2 less than or equal to 2x} It is said that this double integral is equal to zero Why

For double integral, it has the property of function parity, but your formulation is wrong
If the integral region is axisymmetric, the absolute value of the function value at the symmetric point is equal, and the sign is opposite, then the integral is 0. If the function value at the symmetric point is the same, then the integral value is equal to twice of the integral on half region
The axis of symmetry of D = {(x, y): x ^ 2 + y ^ 2 is less than or equal to 2x} is x axis. Whether the integral is 0 depends on what the integrand is and whether it meets the given conditions