Chapter 13: Q 4. (page 1038)

Identify the quantities determined by the integral expressions.
$ρ (x, y)$ is density function.
$\iint_{Ω} x d A and \iint_{Ω} y d A$

Short Answer

Expert verified

The quanitities determined are moments.

Step by step solution

Given Information

It is given that expressions are

$\iint_{Ω} x d A and \iint_{Ω} y d A$

$x, y$ measured in centimeters.

Identification of the quantities

$\iint_{Ω} x d A$ represents first moment about $y$ axis having constant density function $ρ (x, y) = 1$

$\iint_{Ω} y d A$ represents first moment about $x$ axis having constant density function $ρ (x, y) = 1$

Moment will me measured in grams/cm.

Hence, moment about $y$ axis is $M_{y} = \iint_{Ω} x d A$

Moment about $x$ axis is $M_{x} = \iint_{Ω} y d A$

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Identify the quantities determined by the integral expressions.
$ρ (x, y)$ is density function.
$\iint_{Ω} x d A and \iint_{Ω} y d A$

Short Answer

Step by step solution

Given Information

Identification of the quantities

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Identify the quantities determined by the integral expressions.ρ(x,y) is density function.∬ΩxdAand∬ΩydA

Short Answer

Step by step solution

Given Information

Identification of the quantities

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Identify the quantities determined by the integral expressions.
$ρ (x, y)$ is density function.
$\iint_{Ω} x d A and \iint_{Ω} y d A$