$\"\"$

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The equations are $\"\"$ , $\"\"$ on $\"\"$ .

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The value of $\"\"$ .

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Find the intersection points by equating equations.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ and $\"\"$

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

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Consider $\"\"$ and $\"\"$ .

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Apply formula for area of the lamina: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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Find $\"\"$ .

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The moment about the $\"\"$ -axis is $\"\"$ , where, $\"\"$ is uniform density of a planar lamina.

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Substitute $\"\"$ , $\"\"$ , and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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Find $\"\"$ .

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The moment about the $\"\"$ - axis is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ , and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .