$\"\"$

The equation to construct Gateway Arch is $\"\"$ for $\"\"$ .

Differentiate with respect to $\"\"$ .

$\"\"$

Arc length formula : $\"\"$ .

$\"\"$

Using calculator the value of above integral is $\"\"$ .

Therefore, the length of the arch is $\"\"$ .

$\"\"$

Length of the arch is $\"\"$ .