How do you find the volume of the pyramid bounded by the plane 2x+3y+z=6 and the coordinate plane?
the normal vector is
we can re-write the plane as
#z= 0, x = 0 implies y = 2# #z= 0, y = 0 implies x = 3#
the volume we need is
We are going to be performing a triple integral.
The cartesian coordinate system is the most applicable. The order of integration is not critical. We are going to go z first, y middle, x last.
On the plane
We are finding the volume so