This video explains how to find the region of a circle with a missing segment using double integration. This is part 1 of 2 and demonstrates how to formulate the double integrals.
It explains how the region must be split into two parts, the first where the line cuts the circle between an angle of theta = 0 and theta = alpha and then from theta = alpha and theta = 90 degrees. It shows that this involves two double integrals where each integral must be multiplied by 2 to reflect the region below the x-axis
The cartesian coordinates are converted to polar coordinated in order to formulate the integrals.