$\"\"$

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The curve equation is $\"\"$ .

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Graph the curve equation $\"\"$ .

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Graph:

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$\"\"$

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Observe the graph:

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The curve equation is symmetric about $\"\"$ -axis, $\"\"$ -axis and origin.

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

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$\"\"$

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The curve equation is $\"\"$ .

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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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$\"\"$ .

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$\"\"$

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Find the length of the curve in first quadrant.

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Length of the curve $\"\"$ on the interval $\"\"$ is $\"\"$ .

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

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

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$\"\"$

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$\"\"$ .

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$\"\"$

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Graph of the curve equation $\"\"$ :

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$\"\"$

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The curve equation is symmetric about $\"\"$ -axis, $\"\"$ -axis and origin.

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

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