Certroid of area: y = 27.97941, y = sqrt(r^2 - x^2)

[andymorl]

Does anyone know how to find the x-centroid of this shape?

The function of the horizontal line is y = 27.97941

The function of the curve is y = sqrt(r^2 - x^2)

Every time I integrate from the origin I get the wrong answer. I have checked the answer in this link:

http://www.wolframalpha.com/widgets/view.jsp?id=cd5c18dacba13b2e52c1b42580e1d43d

but I cannot get the same answer...

When I integrate I end up with the second attachment for the moment about y. Is this correct? :S

\(\displaystyle \displaystyle \int\, \)\(\displaystyle x\, \left(27.97941\, -\, \sqrt{\strut r^2\, -\, x^2\, }\right)\, dx\)

\(\displaystyle \dfrac{(r^2\, -\, x^2)^{\dfrac{3}{2}}}{3}\, +\, \dfrac{2797941\, x^2}{200000}\, +\, C\)

r = 25.979

x = 22.287

Any help would be much appreciated....

P.S. I know the centroid is around 15m from a worked example...

 

[takahiro4]

1/2I=∫27.9-sqrt(r^2-x^2)dx