$\"\"$

\

The density of each Lamina is $\"\"$ .

\

Region bounded by the rectangle :

\

Observe the graph:

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The height of the rectangle varies from origin to a height of $\"\"$ units.

\

$\"\"$

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The base of the rectangle varies from origin to a distance of $\"\"$ units.

\

$\"\"$

\

The region bounded by the rectangle is $\"\"$ .

\

$\"\"$

\

Evaluate the mass of lamina.

\

The lamina mass can be defined as $\"\"$ .

\

$\"\"$

\

The mass of the lamina is $\"\"$ .

\

$\"\"$

\

Moment of inertia of the lamina :

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The Moment of inertia of the lamina can be defined as

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$\"\"$

\

Where $\"\"$ ,

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$\"\"$ . $\"\"$

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$\"\"$

\

$\"\"$

\

$\"\"$

\

The moment of inertia of lamina is : $\"\"$ .

\

Lamina moment of inertia is verified .

\

$\"\"$

\

The radius of the lamina about y -axis is $\"\"$ .

\

$\"\"$

\

The radius of the lamina about x -axis is $\"\"$ .

\

$\"\"$

\

$\"\"$

\

The moment of inertia of lamina is : $\"\"$ .

\

The radius of the lamina about y -axis is $\"\"$ .

\

The radius of the lamina about x -axis is $\"\"$ .