Chapter 13: Q 5. (page 1038)

Identify the quantities determined by the integral expressions
$ρ (x, y)$ is a density function in grams per square centimeter
$\frac{\iint_{Ω} x d A}{\iint_{Ω} d A} and \frac{\iint_{Ω} y d A}{\iint_{Ω} d A}$

Short Answer

Expert verified

The quantities determines center of mass.

Step by step solution

Given Information

The given expressions are

$\frac{\iint_{Ω} x d A}{\iint_{Ω} d A} and \frac{\iint_{Ω} y d A}{\iint_{Ω} d A}$

$x, y$ is in centimeter.

Identification of the quantities

$\frac{\iint_{Ω} x d A}{\iint_{Ω} d A}$ represents center of mass within region $Ω$ having constant density function $ρ (x, y) = 1$ measured from $y$ axis in centimeters.

$\bar{x} = \frac{\iint_{Ω} x d A}{\iint_{Ω} d A}$

Similarly

$\frac{\iint_{Ω} y d A}{\iint_{Ω} d A}$ represents center of mass within region having constant density function $ρ (x, y) = 1$ measured from $x$ axis.

$\bar{y} = \frac{\iint_{Ω} y d A}{\iint_{Ω} d A}$

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Identify the quantities determined by the integral expressions
$ρ (x, y)$ is a density function in grams per square centimeter
$\frac{\iint_{Ω} x d A}{\iint_{Ω} d A} and \frac{\iint_{Ω} y d A}{\iint_{Ω} d A}$

Short Answer

Step by step solution

Given Information

Identification of the quantities

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Identify the quantities determined by the integral expressionsρ(x,y)is a density function in grams per square centimeter∬ΩxdA∬ΩdAand∬ΩydA∬ΩdA

Short Answer

Step by step solution

Given Information

Identification of the quantities

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Pure Maths

Mechanics Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Identify the quantities determined by the integral expressions
$ρ (x, y)$ is a density function in grams per square centimeter
$\frac{\iint_{Ω} x d A}{\iint_{Ω} d A} and \frac{\iint_{Ω} y d A}{\iint_{Ω} d A}$