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

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The discussion focuses on finding the centroid of the curve defined by x=2-(y^2) and the y-axis. The area calculated is (4/3)(√2), with the centroid coordinates determined as Cx = 4/5 and Cy = 0. A discrepancy arises regarding the calculation method for Cx, where the textbook provides a direct integral solution resulting in [(16/15)√2]. The poster suggests that the textbook likely omitted intermediate steps, implying that a u-substitution could clarify the process. The conversation emphasizes the importance of understanding the integration technique used to arrive at the centroid.
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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?
 
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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.
 

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