$\"\"$

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The equation is $\"\"$ .

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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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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Let length of curve in first quadrant is $\"\"$ then total length of the curve will be $\"\"$ .

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

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

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The total arc length of the astroid is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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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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$\"\"$ units.

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$\"\"$

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$\"\"$ units.