In such an example y with on top y and x with on top x W

Solution

It seems to be true in this case because x and y are related as   x = y^2 and the rod goes to (1, 1 ) m only

which means dx   = 2 y dy

dL   = sqrt(dx^2 + dy^2)   = sqrt(4y^2 + 1) dy

Xcm   =    integral ( x * dL ) dy from 0 to 1 / integral ( dL ) dy from 0 to 1    = 0.41 m

Ycm   =    integral ( y * dL ) dy from 0 to 1 / integral ( dL ) dy from 0 to 1    = 0.574 m