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

Here is the problem:

http://dl.dropbox.com/u/64325990/Photobook/question.PNG [Broken]

Here is the answer:

http://dl.dropbox.com/u/64325990/Photobook/solution.PNG [Broken]

So what the answer says is that you can find the volume under the surface minus the volume of the rectangle with height z=1. However I don't see how this will work for every question. Here I will illustrate why I think their solution will not always be correct:

http://dl.dropbox.com/u/64325990/Photobook/Photo%202012-05-31%205%2004%2056%20PM.jpg [Broken]

As you can see, if it so happens that the max height of the surface is less than 1 then subtracting the rectangle will give you an answer too small. Does anyone agree with me?

For those who are interested, I decided to subtract 1 from the z function and find the surface under z = 1+x^2+(y-2)^2 which also gave the correct answer.

Thank you!

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# Homework Help: Double Integrals: Will this solution always give the correct answer?

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