Question

used triple intergal to calculate the volume of the solid which is bounded by the plane: 2x+3y+z=12 and coordinate planes in the first octant

Answer 1

what grade math is this

Answer 2

multivariate calculus

Answer 3

so solve for x right

Answer 4

first octant implies x,y,z >0
from plane equation, solve for z , set greater than 0
z = 12-2x-3y
--> 12-2x-3y > 0
--> y < (12-2x)/3
set y greater than 0
--> (12-2x)/3 > 0
--> x < 6

therefore we now know our limits:
0<x<6
0<y<(12-2x)/3
0< z < 12-2x-3y
\[\large V = \int\limits_{0}^{6}\int\limits_{0}^{(12-2x)/3}\int\limits_{0}^{(12-2x-3y)} dz dy dx\]
if someone could verify this, that would be great

Answer 5

i get a volume of 24 after integrating everything

Answer 6

its 48 after integrating