- #1

King Tony

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## Homework Statement

Let S be the region in the first octant under the plane 3x + 2y +z = 4. Find the volume of S.

## Homework Equations

idk?

## The Attempt at a Solution

[tex]\int^{\frac{4}{3}}_{0}\int^{\frac{3}{2}x + 2}_{0}\int^{-3x - 2y + 4}_{0}dzdydx[/tex]

= [tex]\int^{\frac{4}{3}}_{0}\int^{\frac{3}{2}x + 2}_{0}(-3x - 2y + 4)dydx[/tex]

= [tex]\int^{\frac{4}{3}}_{0}(-\frac{15}{2}x^{2} - 6x + 4)dx[/tex]

= 448/27

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