- #1

- 261

- 2

**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!