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## Homework Statement

Set up the following as a double integral whose value is the stated volume, express this double in two ways as an iterated integral, and evaluate one of these.

## Homework Equations

Volume, in the first octant, bounded by -

z = 4- (y^2)

x=0

y=0

z=0

3x + 4y =12

## The Attempt at a Solution

Forgive me if I don't know my way completely around conveying the notation online.

y = (12 - 3x)/4

When y = 0, x = 4.

x = (12-4y)/3

when x = 0, y = 3.

I assume that I set up the integral in two ways, one where dA = dy dx and another where dA = dx dy.

[tex]\int[/tex][tex]^{4}_{0}[/tex] [tex]\int^{(12-3x)/4}_{0}[/tex] (4 - y[tex]^{2}[/tex]) dy dx

or

[tex]\int[/tex][tex]^{3}_{0}[/tex] [tex]\int^{(12-4y)/3}_{0}[/tex] (4 - y[tex]^{2}[/tex]) dx dy

and solve? Basically, did I set up the integrals correctly?