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

(1 pt) Find the volume of the region bounded by the planes

2. Relevant equations

V = ∫∫7/4-6/4y-2/4x

3. The attempt at a solution

Since y=x I found their values when z = 0.

6x+2x=7, x=7/8

y= 7/8 is the maximum value y will have in this integration as it decreases as x approaches its maximum value: 2x = 7, x=7/2.

When I made a 2-D image of the region I would be integrating on I came up with a triangle which had two areas that needed to be integrated separately as in the first region: 0≤x≤7/8 and 0≤y≤x, and in the second region: 7/8≤x≤7/2 and 0≤y≤(7/6 - x/3).

After integrating my result was 0.893229167.

What I am wondering is if I am using the correct limits for my integration or if I made a mistake in my math.

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# Volume between given planes

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