Center of Mass and Mass

1. Sep 18, 2016

nysnacc

1. The problem statement, all variables and given/known data

2. Relevant equations
triple integrals, center of mass

3. 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, cuz 0≤ x ≤1 how come it is outside the x limits, or what was the mistake?

2. Sep 18, 2016

LCKurtz

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

3. Sep 18, 2016

Staff: Mentor

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

4. Sep 18, 2016

nysnacc

5. Sep 18, 2016

LCKurtz

6. Sep 19, 2016

ehild

It is wrong. Check your work.

7. Sep 20, 2016

nysnacc

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

8. Sep 20, 2016

Thanks