\

Let the equation of the large circle be $\"\"$ .

\

Then the equation of the small circle is $\"\"$ .

\

Where $\"\"$ is the distance between the centers of the circles.

\

Area of the crescent-shaped region is $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

\

Evaluate the integral $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Evaluate the integral $\"\"$ .

\

Apply the special integral formula :

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Evaluate the integral $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

\

Area of the crescent-shaped region is,

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

\

$\"\"$ .