Final answer:
The given triple integral ∭ᵥdV represents the volume enclosed by the region ᵥ in the space. Since the integral is over the volume element dV, the integral of the constant function 1 over the given region will yield the volume of the region ᵥ.
Step-by-step explanation:
The triple integral ∭ᵥdV represents the integration of a constant function 1 over the region ᵥ. In triple integration, dV represents the volume element. Integrating dV over a region in space gives the volume enclosed by that region. When integrating a constant function over a volume, the result is simply the volume of that region.
The notation ∭ᵥdV indicates a triple integral over the region ᵥ, and dV signifies the infinitesimal volume element within that region. The integral is evaluating the volume by summing up all these infinitesimal volumes throughout the region ᵥ. The concept relies on slicing the region into tiny volumes and summing them to determine the total volume of the enclosed space.
As the integral of dV represents the volume within the region ᵥ, the result of the given integral ∭ᵥdV provides the volume of the specified region in the space. This calculation helps in finding the volume for various shapes and regions defined within three-dimensional space.