I would like to know if my thinking on the problem is correct. I need to find the area between the circles and

After I graphed the 2 circles I looked at them and realized that the area between them is symmetric so I only need to find one half of it and multiply it by 2. So I figured that if I just took the circle and did the integral I would get the area bounded between the two circles. In the end I got

Could someone tell me if I am correct. Thank you.