(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find M_{x},M_{y}, & (x bar, y bar) for the laminas of uniform density ρ bounded by the graphs of the equations. (Use rho for ρ as necessary.)

x=-y

x=5y-y^{2}

2. Relevant equations

m= ∫f(x)-g(x) dx

my= ∫x(f(x)-g(x)) dx =>x bar my/m

mx= 1/2 ∫ (f(x))^{2}-g(x))^{2}dx => y bar=mx/m

3. The attempt at a solution

So this is my work

x=-y <-- g(y)

x=5y-y^2 <----f(y)

a=0

b=6

*note I don't know how to put 0 to 6 on the integral

m=p ∫ [(5y-y^2)-(y)]dy

=p [3y^2 -(y^3/3)]= 36 p

My= p∫[(5y-y^2)+((-y)/2)][(5y-y^2)-(-y)]

=p/2∫ (4y-y^2)(6y-y^2)dy

=p/2∫ (y^4-10y^3+24y^2) dy

= p/2 [(y^5/5)-(5y^4/2)+8y^3]

=216/5 p is wrong I don't know why :?:

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# Moments,Center of Mass, & Centroid

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