Question

Identify the quantities determined by the integral expressions in Exercises 19–24. If x, y, and z are all measured in centimeters and ρ(x, y,z) is a density function in grams per cubic centimeter on the three-dimensional region , give the units of the expression.

${\iiint }_{\mathrm{\Omega }} \left(x^2+z^2\right)\rho (x,y,z)dV$

Short answer

Quantity: radii of gyration

Unit : square centimeter.

Step-by-step solution

Step 1. Given information.

Given:

${\iiint }_{\mathrm{\Omega }} \left(x^2+z^2\right)\rho (x,y,z)dV$

We have to identify the quantities determined by the given integral expression.

Step 2. Identify the quantity

The objective of the problem is to describe about the triple integral ${\iiint }_{\mathrm{\Omega }} \left(x^2+z^2\right)\rho (x,y,z)dV$and find its units.

The given relation represents the radii of gyration and its unit is square centimeter.