calc check
posted by drwls .
<<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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