Triple Integration for Volume: Finding Intersections and Sketching Functions

[Tarhead]

I have a group of problems that deals with the equations:

f(x,y)= x^2+y^2
g(x,y)=20-(x-4)^2-(y+2)^2

Can someone help find the triple integral to find the volume.

 

[Zaphodx57x]

I would start off by making at the very least a rough sketch of the volume you are trying to find, that way you can find out the boundaries you are dealing with.

 

[HallsofIvy]

It might help to clarify the problem: functions don't HAVE a volume!

If you mean "find the volume of the region bounded by z= x²+ y² (a paraboloid) and z= 20- (x-4)²- (y+2)² (also a paraboloid)" then you need to determine where the two paraboloids intersect and "project" that down to the xy-plane.

I get (x+2)²+ (y-1)²= 5, a circle. Subtract the two "z" values and integrate over that circle.

(Please do not post the same question twice!)

 

[Tarhead]

Thanks for the help. I have problems with finding the intersection and projecting that on the x-y plane. We cannot use graphing calculators. Are there any easy ways to sketch the functions and/or find the intersection?