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Find the centroid of the region bounded by the curve x=2-y^2 and the y-axis:

my work shown:

therefore if A= 2 times the integral of sqrt(2-x) dx

is the M_x equal to the integral of (2-x) dx from 0 to 2?

and the M_y equal to the integral of (2)(x)(sqrt(2-x) dx from 0 to 2?

therefore x-coordinate of the centroid is M_y/A

and the y-coordinate of the centroid is M_x/A

therefore centroid is [(M/y/A),(M_x/A)]

is this correct?

then the x-coordinate of the centroid is (M_y / A)

i've been told the centroid of the y-coord. is zero... .however i dont' believe that is correct.. how do i determine the centroid and are M_x and M_y values correct... because if they are ... isn't the centroid simply x--> M_y/A and y--> M_x/A... please help me with this problem!!!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Centroid of the region bounded by the curve...need help

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