$\"\"$

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The function is $\"\"$ .

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Find the arc length of the graph of the function over the interval $\"\"$ .

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Consider $\"\"$ .

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

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$\"\"$

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Find the arclength of the hypocycloid.

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

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$\"\"$

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$\"\"$

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$\"\"$

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Here integrand function has infinite discontinuity at $\"\"$ .

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$\"\"$

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Integral formula : $\"\"$ .

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$\"\"$

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$\"\"$ .

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Arc length of $\"\"$ is $\"\"$ units.

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$\"\"$

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Arc length of $\"\"$ graph is $\"\"$ units.