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

Find the centroid of the solid:

the tetrahedron in the first octant enclosed by the coordinate planes and the plane x+y+z=1.

2. Relevant equations

xcenter = [tex]\frac{\int\int\int_G x dV}{V}[/tex]

ycenter = [tex]\frac{\int\int\int_G y dV}{V}[/tex]

zcenter = [tex]\frac{\int\int\int_G z dV}{V}[/tex]

3. The attempt at a solution

I have shown my attempt for xcenter, as the same problem arises for each one.

[tex]\frac{\int_{x=0}^1\int_{y=0}^1\int_{z=0}^{1-y-x} x dzdydx}{\int_{x=0}^1\int_{y=0}^1\int_{z=0}^{1-y-x} dV} [/tex]

but [tex]\int_{x=0}^1\int_{y=0}^1\int_{z=0}^{1-y-x} dV[/tex] is equal to zero,

so the above expression is undefined.

According to my text, the answer should be (1/4,1/4,1/4). Could someone point out what I did wrong? (Perhaps my bounds of integration?)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Centroid of a Solid (triple integral)

**Physics Forums | Science Articles, Homework Help, Discussion**