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

use triple integral to find the volume of tetrahedron enclosed by the coordinat planes "x=o , y=0 , z=0" and the plane 2x+y+z=0

2. Relevant equations

3. The attempt at a solution

I will integrate the constant function f(x,y,z)=1 by the order : dzdydx

the equation will be : z=-2x-y

so the limits for the inner integral will be from 0 to -2x-y

when z=0 ---> y=-2x

so the limits for the middle integral will be from 0 to -2x

THE PROBLEM HERE IS THAT

when z=0,y=0 ---> x=0 .. !!!!

so the limits for the outer integral will be from 0 to 0 .. !!

and this means the triple integral will be 0 .. !!

so there is no volume ??!

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

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!

# Volume by triple integral

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