$\"\"$

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The curves are $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ and about $\"\"$ axis.

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Method of cylindrical shells:

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

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$\"\"$ , where $\"\"$ .

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Here $\"\"$ .

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

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Substitute corresponding values in volume formula.

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$\"\"$ .

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Consider $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Change in integral limits :

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If $\"\"$ , then $\"\"$ .

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If $\"\"$ , then $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ and change in integral limits in the above integral.

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$\"\"$

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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 $\"\"$ .