Center of Mass and Mass Calculation

[nysnacc]

Homework Statement

Homework Equations

triple integrals, center of mass

The Attempt at a Solution

I set up the triple integral

x: lower limit 0 upper limit 1
y: lower limit 0 upper limit 2
z: lower limit 0 upper limit 1

∫∫∫ δ(x,y,z) dx dy dz
=> applied the limits for x, y and z, and δ(x,y,z) = 2 +xy -2z (given)

I got mass is equal to 1.

Then I tiried to find x bar (x coordinate of center of mass)
set up this way: ∫∫∫ (x * δ(x,y,z) dx) dz dy divide by Mass (Mass = 1 from previous result)

and got x bar = 1.667, which does not make sense, because 0≤ x ≤1 how come it is outside the x limits, or what was the mistake?

 

[LCKurtz]

How are we to know what your mistake is without you showing us your work? Probably a mistake in algebra or integration.

 

[Mark44]

Here's your integral, formatted using LaTeX. Click on it to see what I wrote.
$$\int_{z = 0}^1 \int_{y = 0}^2 \int_{x = 0}^1 2 + xy - 2z \ dx \ dy \ dz$$

 

[nysnacc]

https://www.twiddla.com/vvkzdr

 

[LCKurtz]

https://www.twiddla.com/vvkzdr

Sorry. I won't click on unknown links.

 

[ehild]

∫∫∫ δ(x,y,z) dx dy dz
=> applied the limits for x, y and z, and δ(x,y,z) = 2 +xy -2z (given)

I got mass is equal to 1.

It is wrong. Check your work.

 

[nysnacc]

It is wrong. Check your work.

Realized the problem, should be 3, algebraic mistake :P

 

[nysnacc]

Thanks