A region of the xy plane is defined by the inequalities
(a) the area of the region
(b) The first moment of area about the x-axis,
(c) the coordinates of the centroid of this area.
(d)The volume obtained when this area is rotated completely about the x-axis,
(e) The first moment of volume about the y-axis,
(f) The centroid of this volume.
I found (a) correct, its value is 2.
First moment of area about Ox is
This gives me the correct answer, but when i proceed to (c) i have problems. The x-coordinate of the centroid would be and the y-coordinate would be but the answer is
I also found (d) correctly it is
Now (e) we have First moment of about Oy is
I can do the last one.