$\"\"$

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The variable force to move the object is $\"\"$ , $\"\"$ .

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The work done through one cycle is $\"\"$ .

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In this case $\"\"$ .

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Width $\"\"$ .

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

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$\"\"$ .

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$\"\"$ .

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Find the function values.

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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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$\"\"$

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Substitute $\"\"$ and $\"\"$ values in $\"\"$ .

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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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$\"\"$ .

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$\"\"$ .

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$\"\"$

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Simpsons rule :

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$\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ ft-pounds.

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$\"\"$

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$\"\"$ ft-pounds.