$\"\"$

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

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Graph :

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(1) Draw the coordinate plane.

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(2) Graph the curve $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$

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

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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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$\"\"$

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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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$\"\"$

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Find the value of $\"\"$ :

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$\"\"$

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From the trignometric identity : $\"\"$ and $\"\"$ .

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$\"\"$ .

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From the trignometric identity : $\"\"$ .

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$\"\"$ .

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$\"\"$

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Find the length of the curve.

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Theorem :

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If a curve is described by the parametric equations $\"\"$ and $\"\"$ , $\"\"$

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

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Where $\"\"$ .

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$\"\"$

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Since $\"\"$ ,

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$\"\"$

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$\"\"$

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Apply integration :

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$\"\"$

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

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$\"\"$

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

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Graph of the curve :

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$\"\"$ .