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.

$\"\"$

Formula for integration: $\"\"$ .

Substitute $\"\"$ and $\"\"$ in the above formula.

. $\"\"$

Hyperbolic inverse sine function is defined as, $\"\"$ .

$\"\"$

Solution:

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