Spherical Coordinates: Integrating a Hemisphere/Paraboloid

[Tater]

Homework Statement
The outermost integral is:
-2 to 2, dx

The middle integral is:
-sqrt(4-x^2) to sqrt(4-x^2), dy

The inner most integral is:
x^+y^2 to 4, dz






The attempt at a solution

Drawing the dydx in a simple 2d (xy) plane, it is circular with a radius of 2. So this means that the period(theta) will go from 0 to 2pi. Drawing in 3d (xyz) yields a hemisphere/paraboloid. Now this is where I'm stuck. I don't know what to do after this or how to really tackle this problem. Do I want to attempt to draw a 'slice' of it in the spherical outline with the variables phi, rho, theta? Do I have to look at it a certain way (2d or 3d)? I just don't see what I can do!

Any help or guidance is greatly appreciated!

 

[gabbagabbahey]

You haven't actually said what the question asks you to do..

 

[Tater]

Whoops. Thought I stuck that in there. Anyways, all I have to do is convert it to spherical coordinates (from rectangular to spherical).

 

[gabbagabbahey]

Whoops. Thought I stuck that in there. Anyways, all I have to do is convert it to spherical coordinates (from rectangular to spherical).

I was afraid of that

It is indeed a paraboloid, so $\rho$ and $\phi$ will not be independent the way they would if it was a spherical section...

Try finding the relationship between $\rho$ and $\phi$ for the paraboloid's curved and flat surfaces

 

[ber70]

From my weblog
http://buyanik.wordpress.com/2009/05/02/laplacian-in-spherical-coordinates/"