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Chapter 13: Q. 21 (page 1055)

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

鈭�惟鈥�x蚁(x,y,z)dV

Short Answer

Expert verified

Quantity: First momentum

The unit for momentum is grams centimeter.

Step by step solution

01

Step 1. Given information.

Given:

鈭�惟鈥�x蚁(x,y,z)dV

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

02

Step 2. Identify the quantity

The objective of the problem is to describe about the triple integral 鈭�惟鈥�x蚁(x,y,z)dvand find its units.

By the definition of the first momentum M of the solid惟 the triple integral first

momentum.

Hence the given relation represents the first momentum M of the solid 惟

Since if 蚁represents the density of the solid 惟then 鈭�惟鈥�x蚁(x,y,z)dvrepresents the first momentum.

The unit for momentum is grams centimeter.

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