Find the volume of the solid T enclosed above by the sphere x^2+ y^2 + z^2 = 2 and below by the parabloid x^2 + y^2 = z
The double integral. Possiblly polar coordinates (x = r*cos(theta) y = r*sin(theta)). z = f(x,y)
The Attempt at a Solution
I'm not really sure how to start this one since we have two equations with z. I know we want to find a function to represent z. I was thinking of using the parabloid, so that z = x^2 + y^2 = f(x,y). But I'm not sure of how the sphere comes into play. I also know that the z value is between 0 and root 2 (according to the sphere. And that x and y are bounded by the parabloid. I've tried looking in my calculus for help, but they only use one function with one z in it, not two.
Also, I am supposed to be using a double integral to solve this. Thank you guys in advance for the help!