Method 1: Integrability can be calculated: the integrand function is non-negative, but the integral area is a sphere with the origin as the center, which is symmetrical about any coordinate plane, so the integral is 0.

Method 2, hard product, calculated in spherical coordinate system, integrand function = x 2+y 2+z 2 = r, integral:

∫ dφ∫ dθ∫ r * (r 2 * sinφ) dr, the upper and lower limits of the integral are (-π, π), (0,2π), (0, 1) respectively. It is easy to calculate that the final result is 0. It should be noted that the infinitely small volume dxdydz is converted into r 2 * sin φ d φ d θ dr in the spherical coordinate system.