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chapsticks
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Homework Statement
Find Mx,My, & (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-y2
Homework 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))2dx => y bar=mx/m
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 :?: