Calculus - Center of Mass

Find the exact coordinates of the centroid given the curves: y = 1/x, y = 0, x = 1, x = 2.

X = 1/Area*Integral from a to b: x*f(x)dx
Y = 1/Area*Integral from a to b: [(1/2)*(f(x))^2]dx

How do I find the area for this? Once I know that, is this the correct set up?

X = 1/Area*Integral from 1 to 2: [x*(1/x)]dx
X = 1/Area*[x] evaluated at 1 and 2

Y = 1/Area*Integral from 1 to 2:
Y = 1/Area*[(-1/x] evaluated at 1 and 2.


area= INT y dx =INT dx/x= ln x from 1,2

yES, Those are the correct equations for the first moment.

Ok, thanks for checking and for helping.

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