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## Homework Statement

Find the y-centroid of y=x

^{3}between the x-axis, x=2, where area is 4.

## Homework Equations

y

_{c}= integral of (ydA/A)

dA = g(y)dy

y

_{c}= h/2 * (n+1)/(2n+1)

## The Attempt at a Solution

g(y) = y

^{1/3}

A = 4

y

_{c}= integral of (y*y

^{1/3}/4 dy)

= integral(y

^{4/3}* 1/4 dy)

= 3/7 y

^{7/3}* 1/4

Now since the upper limit is y=8, and lower is y=0, you evaluate this expression between 0 and 8.

= 3/28 * (8)

^{7/3}

= 13.71

So that is the answer I get, but another formula I have is the one using h and n above where h = upper limit = 8, and n = order = 3.

With that, I get the answer of 2.28 which is the answer in the answer key.

My question is, where am I going wrong in the integral?

Thank you for your help!