Use spherical coordinates. evaluate (x2 + y2 + z2)2 dv, b where b is the ball with center the origin and radius 3.

Refer to the diagram shown below.

In spherical coordinates,
r² = x² + y² + z²
x = r sinφ cos θ
y = r sinφ sin θ
z = r cosφ

The element of volume is
dV = r² sinφ dr dθ dφ

Therefore, for the sphere with radius = 3,


The integration yields


  1250π