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calc check

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<<y=(1/A)*integral from a to b of: (1/2)[f(x)]^2 dx >>

If that is the y value of the center of mass, I don't know why the factor (1/2) is there

I also don't agree with your calculation of the x value, which should be 1/(ln 2).

I agree with you that the area is ln 2

find the center of mass of the region bounded by y=(1/x), y=0, x=1, and x=2.

please check what i've done:

x=(1/A)*integral from a to b of: xf(x) dx
y=(1/A)*integral from a to b of: (1/2)[f(x)]^2 dx

x = (1/ln(2))*interal from 1 to 2 of: x[1/x] dx
x = (1/ln(2))*[x] from 1 to 2 = 2.885390082-???

y = (1/ln(2))*integral from 1 to 2 of: (1/2)[1/x]^2 dx
y = (1/ln(2))*(1/2)*[-(1/x)] from 1 to 2 = -0,3606737-???

area = integral of f(x)dx
= integral of (dx/x)
= ln(x)] from 1 to 2
= ln(2)-ln(1)
= ln(2) = area

did i do this correctly? please check. thank you so much! :)

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