$\"\"$

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

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Length of a curve with a polar equation $\"\"$ , $\"\"$ is $\"\"$ .

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$\"\"$ .

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Graph:

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Graph the curve $\"\"$ .

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$\"\"$

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Graph of the curve is drawn for the interval $\"\"$ .

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Observe the graph:

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One loop of the curve is enclosed between the the limits $\"\"$ and $\"\"$ .

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The loop of curve is symmetric about $\"\"$ axis.

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Find the top half in the inertval $\"\"$ , multiply the result by 2.

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$\"\"$ .

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

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and limits of $\"\"$ values in $\"\"$ .

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$\"\"$

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$\"\"$

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Using calculator, $\"\"$ .

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$\"\"$ .

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

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$\"\"$

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