Centroid Of An Area 
The centroid of an area is similar to the center of mass of a body. Calculating the centroid involves only the geometrical shape of the area. The center of gravity will equal the centroid if the body is homogenous i.e. constant density. Integration formulas for calculating the Centroid are: 
When calculating the centroid of a complex shape. Divide the shape up into a combination of known shapes. Then use the the following formula: 
