Final answer:
The student is asked to evaluate a volume integral of a vector field squared over a ball with a radius of 1 centered around the origin, using spherical coordinates.
Step-by-step explanation:
The question is asking to evaluate the triple integral of the squared components of a vector field (x², y², z²) over the volume of a sphere, specifically a ball with radius 1 and centered at the origin. The notation dv suggests that this integral is a volume integral over the solid region B.
Evaluating this integral requires using spherical coordinates, since the region of integration, a ball or sphere, is symmetrical about the origin. The limits of integration will be based on the radius of the sphere, and the triple integral can be simplified using symmetry to avoid redundancy in computation.