Step 1:

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The polar curve is $\"\"$ , $\"\"$

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The length of a curve with polar equation $\"\"$ , $\"\"$ is $\"\"$

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Here $\"\"$ .

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$\"\"$

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

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$\"\"$

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Substitute

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$\"\"$ , $\"\"$ and limits of $\"\"$ in length of the polar curve formula.

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$\"\"$

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Consider $\"\"$ .

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

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$\"\"$

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Change of limits:

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Lower limit: If $\"\"$ , then $\"\"$ .

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Upper limit: If $\"\"$ , then $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and change of limits in the integral.

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$\"\"$

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Solution:

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Length of the spiraling polar curve $\"\"$ is $\"\"$

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.