$\"\"$

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The equation of upper half of the ellipse is $\"\"$ .

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(a) Find the volume of ellipse revolving about $\"\"$ -axis.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The equations are $\"\"$ and $\"\"$ .

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Find the integrating limits by equating equations.

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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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The volume of the solid generated revolving about the $\"\"$ -axis.

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Washer method:

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ 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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The volume of the solid generated revolving about the $\"\"$ -axis is $\"\"$ .

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$\"\"$

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(b) Find the volume of ellipse revolving about $\"\"$ -axis.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The equations are $\"\"$ and $\"\"$ .

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Find the integrating limits by equating equations.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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

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Therefore, $\"\"$ .

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$\"\"$

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The volume of the solid generated revolving about the $\"\"$ -axis.

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Washer method:

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$\"\"$ .

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

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$\"\"$

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$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

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$\"\"$ .

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The volume of the solid generated revolving about the $\"\"$ -axis is $\"\"$ .

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$\"\"$

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(a) The volume of the solid generated revolving about the $\"\"$ -axis is $\"\"$ .

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(b) The volume of the solid generated revolving about the $\"\"$ -axis is $\"\"$ .