$\"\"$

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The region is $\"\"$ about $\"\"$ .

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The region $\"\"$ is the line $\"\"$ that passes through the origin.

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Equation of $\"\"$ with $\"\"$ -unit length is $\"\"$ .

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Find the equation of line $\"\"$ .

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$\"\"$ is the line segment on $\"\"$ axis, so the equation of $\"\"$ line is $\"\"$

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Use disk method to find the volume.

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Method of disk:

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The volume of the solid $\"\"$ is $\"\"$ , where $\"\"$ is the cross sectional area of the solid $\"\"$ .

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$\"\"$ .

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Here the the region $\"\"$ is rotated about the line $\"\"$ that is $\"\"$ axis.

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Radius $\"\"$ .

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Integral limits are $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$

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Volume of the region by rotatating about $\"\"$ is,

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$\"\"$

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Volume of the solid is $\"\"$ .

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$\"\"$

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Volume of the solid is $\"\"$ .