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

by johnq2k7
Tags: bounded, centroid, curveneed, region
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johnq2k7
#1
Mar9-09, 01:36 PM
P: 64
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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Dr.D
#2
Mar9-09, 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.
johnq2k7
#3
Mar9-09, 02:15 PM
P: 64
Quote Quote by Dr.D View Post
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.
i'm confused with what u mean.. do u mean integrate the equation in terms of x instead of y to determine the centroid.. how do i go about doing that...

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 co-ord. of (x,y)

please help

Dr.D
#4
Mar9-09, 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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