Step 1:

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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 is drawn for $\"\"$ .

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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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Let $\"\"$

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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Let $\"\"$

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Differentiate with respect to $\"\"$ .

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$\"\"$

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Change of limits:

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Upper limit:If $\"\"$

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Lower limit:If $\"\"$

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Substitute $\"\"$ and $\"\"$ in Equation (1).

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$\"\"$

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$\"\"$

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Substitute $\"\"$ values in $\"\"$ .

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$\"\"$

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

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