Volume by triple integral

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Homework Statement


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


Homework Equations





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 ??!
 

Answers and Replies

  • #2
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I think there is a mistake in the plane's equation, right ?
If I find the x&y&z intercepts, all will be (0,0,0)
so there is no plane !
Right?
 
  • #3
LCKurtz
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These type of homework problems typically ask for the volume in the first octant ...

Your plane doesn't pass through the first octant because of the 0 on the right side of the equation. To get three positive intercepts you need a positive number on the right, then it will form a tetrahedron with the coordinate planes. Check the problem is copied correctly.
 

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