Find the average value of the squared distance between the o

[gnozahs]

Find the average value of the squared distance between the origin and points in the solid paraboloid D={ (x,y,z): 0 ? z ? 4 - x^2 - y^2}.

I followed the example in the book but this problem looks nothing like the example in the book thus I have no idea on how to approach this problem. If someone could give me a start on how to start this problem, that would be great.

 

[mmm4444bot]

What are the general steps in the example?

 

[galactus]

Re: Find the average value of the squared distance between t

Find the volume of the paraboloid. You can use polar or rectangular.

\(\displaystyle V=\int_{-2}^{2}\int_{-\sqrt{4-x^{2}}}^{\sqrt{4-x^{2}}}(4-x^{2}-y^{2})dydx\)

The distance from the origin to a point on the paraboloid is \(\displaystyle f(x,y)=(x-0)^{2}+(y-0)^{2}=x^{2}+y^{2}\)

The average value of the squared distance is \(\displaystyle f_{ave}=\frac{1}{V}\int\int_{R}f(x,y)dA\)

Can you set up that integral?.