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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...