Look at hand drawn picture below.

As you know the volume is,

Where, is the set of points determined by this tetrahedron.

By Fubini's theorem it can be computed as,

Where,

is the lower surface bound on the tetrahedron in this case and is the equation of the plane above. To find the equation of that plane we need to find the equation of the plane passing through the points:

, , and

I am not going to find the equation of the plane that is for thee to find.

Next, you need to express the region as Type I and Type II:

In that case,

And,

Again where,

Is the equation of plane expressed in terms of