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

A solid "rough" of constant density ([tex]\delta[/tex] =1) is bounded below by the surface z=4y^2,above by the plane z=4, and one the ends by the planes x=1 and x=-1. Find the center of mass...

2. Relevant equations

[tex]_{M}[/tex]xy =[tex]\int\int\int[/tex] z [tex]\delta[/tex] dV

Mass = [tex]\int\int\int[/tex][tex]\delta[/tex]dV

then to find the center of mass, the z component would be [tex]_{M}[/tex]xy / M

3. The attempt at a solution

[tex]_{M}[/tex]xy = [tex]\int\int\int[/tex][tex]^{4}_{4y^2}[/tex] z [tex]\delta[/tex]dzdydx

=[tex]\int\int[/tex] [z^2/2][tex]^{4}_{4y^2}[/tex]dydx

=[tex]\int[/tex][tex]^{1}_{-1}[/tex][tex]\int[/tex][tex]^{1}_{0}[/tex](8-8y^4)dydx

=8[tex]\int^{1}_{-1}[/tex][y-y^5/5][tex]^{1}_{0}[/tex] dx =8[tex]\int[/tex][tex]^{1}_{-1}[/tex][4/5]dx

=8[4x/5][tex]^{1}_{-1}[/tex] = 8[4/5+4/5]= 64/5

For some reason, and it isn't obvious to me why, the solution manual says that this answer should be 128/5. i'm off by a factor of 2, but i don't know what i did wrong. I haven't attempted to find the mass yet, but i think once i understand what I did wrong here, that answer shouldn't be hard to find.

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# Homework Help: Center of mass and integrating

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