Center of mass and integrating

[flame_m13]

Homework Statement

A solid "rough" of constant density ($$\delta$$ =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...

Homework Equations

$$_{M}$$xy =$$\int\int\int$$ z $$\delta$$ dV
Mass = $$\int\int\int$$$$\delta$$dV
then to find the center of mass, the z component would be $$_{M}$$xy / M

The Attempt at a Solution

$$_{M}$$xy = $$\int\int\int$$$$^{4}_{4y^2}$$ z $$\delta$$dzdydx
=$$\int\int$$ [z^2/2]$$^{4}_{4y^2}$$dydx
=$$\int$$$$^{1}_{-1}$$$$\int$$$$^{1}_{0}$$(8-8y^4)dydx
=8$$\int^{1}_{-1}$$[y-y^5/5]$$^{1}_{0}$$ dx =8$$\int$$$$^{1}_{-1}$$[4/5]dx
=8[4x/5]$$^{1}_{-1}$$ = 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.

 

[HallsofIvy]

Why are you integrating, with respect to y, from y= 0 to y= 1? The "cylinder" z= 4y² intersects the plane z= 4 at y= -1 and 1.

 

[flame_m13]

Why are you integrating, with respect to y, from y= 0 to y= 1? The "cylinder" z= 4y² intersects the plane z= 4 at y= -1 and 1.

i don't know why that didn't register with me. thanks for pointing that out. my answer is now 128/5, the same as the book's.