I need help setting the bounds of this equation

Find the volume of the solid bounded by the planes x=0 y=0 z=0 and x+y+z=6

thank you

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- Nov 19th 2008, 07:06 AMkoalamathintegration
I need help setting the bounds of this equation

Find the volume of the solid bounded by the planes x=0 y=0 z=0 and x+y+z=6

thank you - Nov 19th 2008, 07:33 AMSoroban
Hello, koalamath!

Quote:

Find the volume of the solid bounded by the planes: .$\displaystyle x+y+z\:=\:6,\;x=0,\;y=0,\;z=0$

The solid is in the first octant, bounded by the plane $\displaystyle x + y + z \:=\:6$

. . which has intercepts: (6,0,0), (0,6,0), (0,0,6).

We have: .$\displaystyle V \;=\;\int\int_A z\,dA$ . . . where $\displaystyle A$ is the region in the $\displaystyle x\text{-}y$ plane.

That region looks like this:Code:`|`

6 *

|:*

|:::*

|:::::*

|:::::::*

|:::::::::*

- + - - - - - * - - -

| 6

We see that $\displaystyle y$ goes from $\displaystyle 0$ to $\displaystyle 6-x$

And $\displaystyle x$ goes from $\displaystyle 0$ to $\displaystyle 6.$

Therefore: .$\displaystyle V \;=\;\int^6_0\int^{6-x}_0 (6-x-y)\,dy\,dx$

- Nov 19th 2008, 10:35 AMkoalamath
Thank you so much

- Nov 19th 2008, 10:44 AMkoalamath
Wait i get 6 as the answer and that's wrong

- Nov 19th 2008, 12:36 PMKrizalid
Your integration skills or arithmetic are wrong 'cause the answer is 36.