Centroid of a bounded region: Help

[x31fighter]

Homework Statement

Find the centroid of the region bounded by the graphs of y = sqrt (x) and y = (1/2) * x

Homework Equations

A = [f(x)-g(x)]dx
from point a -> b

The Attempt at a Solution

x = [0,4] ; p(0,0) and p(4,2)

I am just checking on if I did the integral correctly.

A = ((2x^3)/3) - ((x^2)/4)] 0 -> 4

 

[Mark44]

Homework Statement

Find the centroid of the region bounded by the graphs of y = sqrt (x) and y = (1/2) * x

Homework Equations

A = [f(x)-g(x)]dx
from point a -> b

The Attempt at a Solution

x = [0,4] ; p(0,0) and p(4,2)

I am just checking on if I did the integral correctly.

A = ((2x^3)/3) - ((x^2)/4)] 0 -> 4

Not quite. If you integrate x^1/2 you don't get x³.