Finding coordinates of a centroid

[hahaha158]

Homework Statement

Find the exact coordinates of the centroid for the region bounded by the curves x=5-y^ 2 and x=0

I am not sure about this one because it uses dy instead of dx i think.

I tried to set it up like this

x= [0.5∫(5-y^2)^2 dy from -5 to 5]/[ ∫(5-y^2)dy from y=-5 to 5]

This does not give me the right answer, can anyone help? I have no trouble solving it if it gives me a region bounded by y=x (for example), but i think that the centre of mass in y-variable means that Mx and My are reversed?

Very confused, thanks for any help you can give

Homework Equations

x=My/A
y=Mx/A

The Attempt at a Solution

 

[haruspex]

x= [0.5∫(5-y^2)^2 dy from -5 to 5]/[ ∫(5-y^2)dy from y=-5 to 5]

Why the 0.5 at the front?
Also, you have the wrong range for y.

 

[hahaha158]

Why the 0.5 at the front?
Also, you have the wrong range for y.

i added the 0.5 because i tried using the My equation for centre of mass in y-variable whch is density/2∫[f(y)^2-g(y)^2]dy from a to b. Would the range be -5^.5 to 5^.5?