Homework Help: Integration of a function.

1. Nov 12, 2008

stanford1463

1. The problem statement, all variables and given/known data
Hey guys, I have one question: how can I integrate the function f(x,y,z)=x + y + z over the region between the paraboloid 4-x^2-y^2 and the xy-plane?

2. Relevant equations
For the paraboloid region, I used polar coordinates and found the volume of the region to be 8pi. Now, I have to find the integration of the other function x+y+z in this.

3. The attempt at a solution
Alright, I tried using a triple integral to no avail (rcos($$\theta$$) +rsin(theta) +z)r drd(theta) dz. I do not know the limits of integration (hardest part of the problem for me). Is there anyway to solve this with only a double integral? Or would I have to use cylindrical/polar whatever triple integration to solve it? Thanks..!

2. Nov 12, 2008

HallsofIvy

How could you find the volume if you don't know the limits of integration? If it was because you integrated
$$\int\int (4- x^2- y^2) dA= \int\int (4- r^2) r dr d\theta[/itex] then you should be able to see that is the same as [tex]\int\int\int_0^{4-x^2-y} dz dA= \int\int\int_0^{4- r^2} r dzdrd\theta$$

3. Nov 12, 2008

stanford1463

ohh....but how is the triple integral from 0 to 4-x^2-y^2 ? I know it's the function, but graphically, I don't understand. Oh well, my homework was due 10 minutes ago and I just turned it in (leaving this question blank) lol. Thanks for the answer though!