Setting
, we see that the two curves intersect at
(as well as
, which is to the left of the
-axis and therefore irrelevant).
The horizontal moment is
while the vertical moment is
Note that the last integral could also be evaluated as
Using the fact that
- The centroid of area
![{\displaystyle A={\frac {1}{A}}({\text{The horizontal moment}},{\text{The vertical moment}}),}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/94854b04b3ae93231e421d82eebaa997c30840e1)
the centroid is therefore
.