I have a homework problem that is not in my book, this is the closest example i found in the book. but i am having trouble doing the integration to find the area and the distance of the Y centroid from the x axis.
The problem states, Locate the centroid of the Semi-elliptical area shown.
The picture is

According to some tables that i found,
Area = (πab)/2

=0
and

= (4b)/3π
Using the table equations i can easily find the area and centroid location, but i am having trouble doing the integration and getting the answer the table equation gives me.