$\"\"$

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The curve is $\"\"$ , $\"\"$ and $\"\"$ .

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Length of the curve: $\"\"$ .

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

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$\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Product rule of derivatives: $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$ $\"\"$

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$\"\"$

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Simpson $\"\"$ s rule:

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

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The Simpson $\"\"$ s Rule for approximating $\"image\"$ is given by

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$\"\"$

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where $\"image\"$ and $\"\"$ .

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$\"\"$

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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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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute all above values in equation $\"\"$ .

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$\"\"$

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$\"\"$

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Arc length of the curve is $\"image\"$ .

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By using calculator the value of

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$\"\"$ .

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Above value is very closer to the Simpson $\"\"$ s approximation.

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$\"\"$

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Using simpson $\"\"$ s rule, arc length of the curve $\"\"$ is $\"\"$ .

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Using calculator, arc length of the curve $\"\"$ is $\"\"$ .