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Homework Statement
Evaluate [itex]\iiint z^2 \,dx\,dy\,dz[/itex] over domain V, where V is the solid defined by
[tex]1 \leq x+y+3z \leq 2[/tex][tex]0 \leq 2y-z \leq 3[/tex][tex]-1 \leq x+y \leq 1[/tex]
Homework Equations
The Attempt at a Solution
I know how to do simple triple integrals, but all the variables in the inequalities are tripping me up. I tried fumbling with the inequalities to find [tex]-y-1 \leq x \leq 1-y [/tex][tex]\frac{z}{2} \leq y \leq \frac{3+z}{2}[/tex][tex]\frac{1-x-y}{3} \leq z \leq \frac{2-x-y}{3}[/tex] but quickly realized that if I just did that, my solution would have x and y variables in it. Basically, I'm not sure about what else my first step should be to fully isolate at least one of the variables.