(adsbygoogle = window.adsbygoogle || []).push({}); The Problem

Evaluate the surface integral of

[tex]

G(x, y, z) = \frac{1}{1 + 4(x^2+y^2)}

[/tex]

where [itex]z[/itex] is the paraboloid defined by

[tex]

z = x^2 + y^2

[/tex],

from [itex]z = 0[/itex] to [itex]z = 1[/itex].

My Work

I rewrote [itex]G(x, y, z)[/itex] as

[tex]\frac{1}{1+4z}[/tex].

Then, I evaluated the surface integral (I'm skipping a few steps in the evaluation here):

[tex]

\int \!\!\! \int_R \frac{1}{1+4z} \sqrt{1+4z} \,dA = \int \!\!\! \int_R \frac{1}{\sqrt{1+4z}}

[/tex].

My Confusion

I do not understand how to evaluate this integral properly. I am not experienced in multiple integration, but I have not found an issue with it until now.

Basically, what are my differential elements supposed to be ([itex]dx, dy[/itex]?). Am I supposed to use polar coordinates here?

If someone could put me on the correct track, I would appreciate it. Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Need Help with Surface Integral

**Physics Forums | Science Articles, Homework Help, Discussion**