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???

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- July 6th 2008, 08:45 PMchris25volume of paraboloid
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??? - July 6th 2008, 10:14 PMChris L T521
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: .

http://img.photobucket.com/albums/v4...LT521/Circ.jpg

(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 - July 7th 2008, 12:42 AMJhevon