Computing center of mass in triple integral

[Win_odd Dhamnekar]

Find the center of mass of the solid S with the given density function $\displaystyle \delta(x,y,z)$

$$S=\{(x,y,z): 0 \leq x \leq1, 0 \leq y \leq 1, 0 \leq z \leq 1-x-y\}, \delta (x,y,z)= 1$$
How to answer this question?

When I tried to compute M, I got M=0.

How is that?

 

[Deleted member 4993]

Find the center of mass of the solid S with the given density function $\displaystyle \delta(x,y,z)$

$$S=\{(x,y,z): 0 \leq x \leq1, 0 \leq y \leq 1, 0 \leq z \leq 1-x-y\}, \delta (x,y,z)= 1$$
How to answer this question?

When I tried to compute M, I got M=0.

How is that?

Please show your work in detail so that we can catch your mistake.

 

[nasi112]

You did this.

$\displaystyle M = \int_{0}^{1}\int_{0}^{1}\int_{0}^{1-x-y} dz \ dy \ dx$

You should do this.

$\displaystyle M = \int_{0}^{1}\int_{0}^{1-x}\int_{0}^{1-x-y} dz \ dy \ dx$