## anonymous 5 years ago Find the volume of the region between the graph of f(xy)=36−x^2−y^2 and the xy plane. I'm not too sure how to set up the double integral-- but 36-x^2-y^2 is what we will integrate? right??

1. anonymous

the x will surely go from 0 till 6

2. anonymous

or maybe from -6 to 6

3. anonymous

ok I guess I have an idea

4. anonymous

the level surface of this is always a circle

5. anonymous

when we look at the xy plane it is a circle with center (0,0) and radius 6

6. anonymous

so x goes from -6 to 6 and y goes from

7. anonymous

would we then use x^2 + y^2 = r^2 to solve for y?

8. anonymous

$-\sqrt{36-x ^{2}}$ to $\sqrt{36-x ^{2}}$

9. anonymous

hmm this cannot be good... damn it would mean that the integral is 0

10. anonymous

I'm going to think about it over dinner-- will be back in 20 min

11. anonymous

ok, I am going to bed soon