Step 1:

\

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

\

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

\

Here $\"\"$ .

\

$\"\"$

\

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

\

$\"\"$

\

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

\

$\"\"$

\

Consider $\"\"$ .

\

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

\

$\"\"$

\

Change of limits:

\

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

\

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

\

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

\

$\"\"$

\

Solution:

\

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

\

.