Does the Hubble Profile of Surface Brightness Lead to Infinite Total Luminosity?

[Logarythmic]

Homework Statement

Show that the Hubble profile of surface brightness

I(r) = I_0 \left(1+\frac{r}{R}\right)^{-2}

leads to an infinite total luminosity. r is the distance from the center and R is a constant.


2. The attempt at a solution
For large r this is related as

I(r) \propto r^{-2}

but how is the surface brightness related to the total luminosity?

 

[dextercioby]

Can't you find it in the textbook ? Even though the problem seems to be purely mathematical (basically a computation which gives infinity as its result), you have problems in the conceptual domain. Well, the/my advice is to look again in the book.

 

[Logarythmic]

I have, all there is about this is one half page of text.

 

[Logarythmic]

This is still a problem... Haven't anyone dealt with this before?