$\"\"$

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The curve equation is $\"\"$ ,lines are $\"\"$ , $\"\"$ and $\"\"$ and the region is rotated about $\"\"$ -axis.

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Method of Cylinders :

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The volume of the solid obtained by rotating about $\"\"$ -axis, the region of the curve $\"\"$ from $\"\"$ to $\"\"$ is

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$\"\"$

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Hence the curve is $\"\"$ .

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$\"\"$

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Find the volume obtained by rotating region about $\"\"$ -axis, bounded by the curve $\"\"$ and $\"\"$ from $\"\"$ to $\"\"$ is

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$\"\"$

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$\"\"$

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$\"\"$

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Volume obtained by rotating region about $\"\"$ -axis is $\"\"$ .

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$\"\"$

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Volume obtained by rotating region about $\"\"$ -axis is $\"\"$ .