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

Hi, I've been trying this for days now and I really can't get it, so would appreciate some help please!

Find the volume of the finite region between the two surfaces z=x^2 + 4y^2 and z=2x + 8y + 4

2. Relevant equations

3. The attempt at a solution

I tried to do a double integral of (x^2 + 4y^2 - 2x - 8y - 4)dxdy. I thought the bounds of this on the x-y plane would be given by x^2 + 4y^2=2x + 8y + 4. However doing this gives a nasty quadratic for x in terms of y that makes things impossible. I'm also pretty sure I need to sub in something of the form x=a*r*cosP, y=b*r*sinP. The Jacobian for this would be abr.

I got thie bound to be between x=1-[5+8y - 4y^2] and 1 + [5+8y - 4y^2] and y = -0.5 and 5/2

I think this is wrong!

I tried subbing in the sin and cos things also, but don't know how to work out the bounds.

Please help!

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# Homework Help: Multiple Integrals

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