$\"\"$ \ \

\

The region bounded by graphs $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ . \ \

\

The volume of the solid is $\"\"$ . \ \

\

Consider $\"\"$ . \ \

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In this case $\"\"$ . \ \

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Width $\"\"$ . \ \

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

\

$\"\"$ .

\

$\"\"$ . \ \

\

Calculate the $\"\"$ at the interval boundaries.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

\

$\"\"$

\

Simpsons rule :

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ to $\"\"$ values. \ \

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ . \ \

\

The volume of the solid is $\"\"$ . \ \

\

$\"\"$

\

The volume of the solid is $\"\"$ . \ \