Question

set up a triple integral that gives the volume of the solid bounded by the coordinate planes and the plane 3x + 2y -z = 6

Answer 1

x =0 , y = 0, z = -6
y = 0, z = 0, x = 2
x = 0, z= 0, y =3

\[\int\limits_{-6}^{0}\int\limits_{0}^{3}\int\limits_{0}^{2} 1 dx dy dz\]

Answer 2

done

Answer 3

No. That integral is the volume of a box. But the volume you want is some kind of triangular pyramid.

So you need to be much more subtle with the limits of integration.