Calculating the Centroid of x=2-(y^2) and the Y Axis

[adelaide87]

Homework Statement

Easy question:

Find the centroid of x=2-(y^2) and the y axis

Homework Equations

The Attempt at a Solution

Already calculated, I got an area of (4/3)(√2)

Cx = 4/5
Cy = 0

When calculating Cx, in the book they have:
Integral (x)(√(2-x))

And go straight to this answer:
[(16/15)√2)].

When I did it, I did it the longer way but got the same thing, how in 1 step do they get this answer?

 

[LCKurtz]

They probably didn't do it in one step, they just didn't show their work. You would do that integral with a u substitution u = 2-x or u²=2-x.