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??

Question

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??

anonymous · Answer

the x will surely go from 0 till 6

anonymous · Answer

or maybe from -6 to 6

anonymous · Answer

ok I guess I have an idea

anonymous · Answer

the level surface of this is always a circle

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

ok, I am going to bed soon