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Homework Help: Luminosity integral help

  1. Feb 8, 2007 #1
    If the total luminosity is given by

    [tex]L_T = \int_0^{\infty} e^{-(r/a)^{1/4}} r^2 dr[/tex]

    estimate the radius [tex]r(a)[/itex] corresponding to half of the total luminosity.

    This would be to integrate from zero to r and get a function [itex]r(a,L)[/itex] but this is impossible so anyone got an idea on how to estimate this?
  2. jcsd
  3. Feb 8, 2007 #2


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    Well the primitive of the integrand exists, you knew that right?

    The difficult part is solving for [itex]r_{1/2}[/itex] in [tex]\int_0^{r_{1/2}} e^{-(r/a)^{1/4}} r^2 dr=L_T/2[/tex]. But computers are good with this.
    Last edited: Feb 8, 2007
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