Let the pyramid with vertices $A(0,0,0), B(0,0,1), C(0,1,0), D(1,1,0)$.
I need to find the equations of the four planes bounding the pyramid then I have to set up an integral for the volume in three ways: $$ dzdydx \quad\text{and}\quad dxdzdy \quad\text{and}\quad dydxdz. $$
So far, I found the equations of the four planes by finding the equations for $ACD$, $ABD$, $ABC$, and $BCD$. The equations I got were $-z$, $-x+y$, $-x$, and $-y-z$. I'm not even sure if that is correct, and from there I'm not sure how to set up the integral.