Question

Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (1,0,0),(0,2,0),(0,0,3)

Answer 1

steps:

find the equation of that plane first.

and write it as z = f(x,y).

then integrate over that region

Answer 2

alright let me see if I can get this equation.

Answer 3

i make it 6x + 3y + 2z = 6

you should check that though or we will be chasing our tails forever!!

Answer 4

lol I only have the final answer for this

Answer 5

I think I can see how you got that.

Answer 6

When I first did this problem I thought it was simply....
\[\int\limits_{0}^{1}\int\limits_{0}^{2}\int\limits_{0}^{3}dzdydx\]

Answer 7

no that is for a cube

same problem.....we need to the limits of integration right......

Answer 8

so this region is pretty much a rectangular prism

Answer 9

here we have a triangle again, on the xy plane

Answer 10

the shaded area is our region. we are integrating \(z = f(x,y) =\frac{1}{2}( 6 - 6x - 3y)\) over that region

Answer 11

man i'm having a really hard time getting to visualize these