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Centroid of the region bounded by the curve...need help 
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#1
Mar909, 01:36 PM

P: 64

Find the centroid of the region bounded by the curve x=2y^2 and the yaxis:
my work shown: therefore if A= 2 times the integral of sqrt(2x) dx is the M_x equal to the integral of (2x) dx from 0 to 2? and the M_y equal to the integral of (2)(x)(sqrt(2x) dx from 0 to 2? therefore xcoordinate of the centroid is M_y/A and the ycoordinate of the centroid is M_x/A therefore centroid is [(M/y/A),(M_x/A)] is this correct? then the xcoordinate of the centroid is (M_y / A) i've been told the centroid of the ycoord. 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 


#2
Mar909, 02:10 PM

P: 619

Why not work out your integrals on y instead of x, 2<=y<=+2?
Then just work the problem out and see what you get without worrying in advance what it is supposed to be. 


#3
Mar909, 02:15 PM

P: 64

isn't my A(y) value correct, i just need help with my values for M_y, M_x assuming my A(y) is correct therefore i could find the centroid as M_y/A,M_x/A for coord. of (x,y) please help 


#4
Mar909, 02:48 PM

P: 619

Centroid of the region bounded by the curve...need help
The given boundary function is x = f(y), so you can calculate the area and the moments as integrals that involve things like
A = int(x) dy from 2 to 2, etc. 


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