$\"\"$

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(a)

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The curves are $\"\"$ , $\"\"$ and $\"\"$ and the region is rotated about $\"\"$ .

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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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Here rotation is about the line $\"\"$ .

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Height is $\"\"$

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Hence the radius is $\"\"$ .

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

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Set up the integral for the volume using above volume formula.

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Here $\"\"$ , $\"\"$ and $\"\"$ .

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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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(b)

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Use calculator to find $\"\"$ .

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Therefore the result is $\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ .

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