Integrating f(x,y,z): Confirm Ranges for x, y, z

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SUMMARY

The discussion centers on the integration of the function f(x, y, z) = x^2 over a tetrahedron G defined by the coordinate planes and the plane x + y + z = 1. The user initially sets the integration limits for z from 0 to 1-x-y, for y from 0 to 1-x, and for x from 0 to 1. After confirming the integration setup, the user realizes that the error lies in the integration process rather than the limits, leading to the conclusion that the ranges were indeed correct.

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Homework Statement



f(x, y, z) = x^2 ; G is tetrahedron bounded by the coordinate planes and the plane octant with equation x + y + z = 1

∫ ∫ ∫ x^2 dzdydx

I try to set up the ranges for x, y and z..

x+y+z = 1
z = 1-x-y...set the limits for z from z=0 to z = 1-x-y

x+y+z = 1
if, z = 0, y = 1-x ...set the limits for y = 0 to y = 1-x

x+y+z = 1
if, z = 0 , y = 0 ...x = a set the limits from x = 0 to x =1

first.. i need help to confirm that my ranges are correct..
because.. I've done the integration and got the wrong answer..
i've double checked my integration and it is right..
there must be something wrong with my ranges.. i guess...
 
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They look right to me. Why don't you show what you did. It may be an integration error.
 
yup2.. it's integration error.. duuhh...~
thanks btw..
problem solved..
 

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