find the volume of the paraboloid z=x^2+y^2 below the plane z=4.
i am stuck on setting up the integral..can any one help???
Let the cross section of the paraboloid at z=4 be our region R.
Thus, the x and y limits of integration become pretty obvious: .
(this is the region R)
Thus, our volume integral would be .
We can also represent this integral in polar coordinates. Note that the limits of integration change!
This time we see : .
As a result, the integral becomes .
Hope that this makes sense!
--Chris