# Math Help - Calculate the volume of the tetrahedron

1. ## Calculate the volume of the tetrahedron

for this problem :

Calculate the volume of the tetrahedron whose vertices are y=0, z=0, x=0 και y-x+z=1

this integral is it the corect one ?

$\int_{x=0}^{1}\int_{y=0}^{-y+1}\int_{z=0}^{z=x-y+1}dG=\int_{0}^{1}\int_{y=0}^{-y+1}(x-y+1) dydx$

2. ## Re: Calculate the volume of the tetrahedron

They both look fine to me...

3. ## Re: Calculate the volume of the tetrahedron

Are you sure of that plane?
Because when you let z equal zero it makes a odd slice in the xy plane
It's y=1+x which isn't going to give you a closed region with the x and y axis.