$\"\"$

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The parametric equations of the curve are $\"\"$ .

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The interval is $\"\"$ .

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Length of the curve with parametric equations $\"\"$ and $\"\"$ , $\"\"$ is $\"\"$ .

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Consider $\"\"$ .

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Differentiate with respect to $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Differentiate with respect to $\"\"$ .

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and limits of $\"\"$ in formula.

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$\"\"$

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Simpsons rule:

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Let $\"\"$ be continuous on $\"\"$ let $\"image\"$ be an even integer,

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The Simpsons Rule for approximating $\"\"$ is given by

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$\"\"$ ,

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where $\"\"$ and $\"\"$

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Here $\"\"$ .

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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 above values in Simpsons formula.

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$\"\"$

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$\"\"$

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$\"\"$

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The length of the curve is $\"\"$ .