Find the Center of Mass of a Circular Region with a Missing Segment using Double Integration

This video evaluates the double integrals, utilizing polar coordinates, found in the video. https://youtu.be/whbt-SnV0Dw It then proceeds to use the results to find the center of mass of a circle with a missing segment. The inner integrals are evaluated first along r summing all the infinitesimally small slices dr, followed by the evaluation of the outer integral from 0 to alpha and then from alpha to pi/2. This sums all the infinitesimally small slices of d(theta). The results of the double integrals are then summed. This gives the weighted average of x over the uniform region. Dividing this by the area of the region gives the center of mass of the region. The calculations re check by setting appropriate values for a and b.