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## Homework Statement

Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0, and x + y + z = 9.

## Homework Equations

. . . ?

## The Attempt at a Solution

After drawing out the picture with z=0 I have a line going from 0,9 to 9,0 bounded by the x and y axis giving me a triangle.

Based on that I got the following domains.

0 <= x <= 9

0 <= y <= 9-x

Which I then use for the following double integral

[tex] \int^{9}_{0}\int^{9-x}_{0} 9 - x - y dy dx [/tex]

After the first integration I get.

9y-(y

^{2})/2-x

After plugging in the limits and simplifying I get 81/2-x^2-x

After integrating the above I get: 81/2x-x

^{3}/3-x

^{2}/2

and plugging and chugging gives me 81 which is wrong. So . . . did I do my domain wrong or it is an integration mistake?