Using polar coordinates to find the volume of a bounded solid

[paraboloid]

Using polar coordinates to find the volume of a bounded solid[Solved]

I found the equation of the boundary circle by setting z to 4 in the paraboloid.
Then I did some work to get polar coords:
$$x^2+y^2 = 1$$
$$x^2+y^2 = r^2$$
$$1-x^2-y^2 = 1-r^2$$
Then I set up my integral as such
$$\int_0^{2\pi}\int_{0}^{1}(1-r^2)rdrd\theta$$
After the double integration, I get pi/2.

edit: It should be 4r-4r³ as the integrand.

 

[vela]

Why are you plugging 1-r² in as the integrand? What are z_upper and z_lower?

 

[paraboloid]

Why are you plugging 1-r² in as the integrand? What are z_upper and z_lower?

I think that's the root of my problem. I found a http://answers.yahoo.com/question/index?qid=20080327174835AA36kOs" that's similar, but it doesn't show the work to get the integrand.

 

[vela]

Draw a sketch of the volume you're integrating. It'll help you visualize what goes where.