$\"\"$

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The curve is $\"\"$ over the interval $\"\"$ .

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Definition of the arc length:

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If the curve $\"\"$ , $\"\"$ , then the length of the curve is defined as $\"\"$ .

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Find $\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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The product rule of derivative : $\"\"$ .

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consider $\"\"$ 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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Arc length of the curve $\"\"$ :

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

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$\"\"$

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$\"\"$

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$\"\"$ \ \

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Consider $\"\"$ then $\"\"$ .

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$\"\"$

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$\"\"$ .

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If $\"\"$ then $\"\"$ .

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If $\"\"$ then $\"\"$ .

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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 arclength of the curve is $\"\"$ .

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$\"\"$

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