# calc check

posted by .

<<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! :)

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### calc

also: integral of tan^(-1)y dy how is integration of parts used in that?
2. ### calc asap!

can you help me get started on this integral by parts?
3. ### calc check: average value

Find the average value of the function "f(x) = x^2 sqrt(1+x^3)" on the interval [0,2]. and this is what i did.. please check for mistakes. thanks :D f(x) = x^2 sqrt(1+x^3), [0,2] f ave = (1/(b-a))*inegral of a to b for: f(x) dx f ave …
4. ### calc: avg value

Find the average value of the function "f(x) = x^2 sqrt(1+x^3)" on the interval [0,2]. and this is what i did.. please check for mistakes. thanks :D f(x) = x^2 sqrt(1+x^3), [0,2] f ave = (1/(b-a))*inegral of a to b for: f(x) dx f ave …
5. ### calc 2

Determine whether the integral converges or diverges. Find the value of the integral if it converges. The integral where b=2 and a=0 (x/x^2-1 dx).
6. ### Calc

Evaluate the integral using any method: (Integral)sec^3x/tanx dx I started it out and got secx(1tan^2x)/tanx. I know I just have to continue simplifying and finding the integral, but I'm stuck on the next couple of steps. Also, I have …
7. ### Quick calc question

Suppose the integral from 2 to 8 of g of x, dx equals 13, and the integral from 6 to 8 of g of x, dx equals negative 3, find the value of 2 plus the integral from 2 to 6 of g of x, dx. 16 18 8 32
8. ### Quick calc question

Suppose the integral from 2 to 8 of g of x, dx equals 13, and the integral from 6 to 8 of g of x, dx equals negative 3, find the value of 2 plus the integral from 2 to 6 of g of x, dx. 16 18 8 32
9. ### calc

Sketch the regions represented by the following integrals and evaluate them using geometric formulas. 4 integral 1: 2x+3dx 6 integral -2: lx-1l dx (absolute value of x-1
10. ### Calc

Suppose the integral from 2 to 6 of g of x, dx equals 12 and the integral from 5 to 6 of g of x, dx equals negative 3 , find the value of the integral from 2 to 5 of 3 times g of x, dx

More Similar Questions