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!