(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Volume, in the first octant, bounded by -

z = 4- (y^2)

x=0

y=0

z=0

3x + 4y =12

3. 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?

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# Homework Help: Some double integrals

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