1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Black Body Radiation (Awkward integral)

  1. Jun 2, 2010 #1
    1. The problem statement, all variables and given/known data
    What percentage of the Sun’s blackbody radiation spectrum falls into the visible light spectrum (400-700 nm). Where T=5000K
    Hint: Integrate over frequencies

    2. Relevant equations
    B=2h[tex]\nu[/tex]3c-2 (eh[tex]\nu[/tex]/kT-1)-1

    Where [tex]\nu[/tex] is the frequency of the light.
    3. The attempt at a solution

    Ok so the problem is very straightforward, i'm just having trouble evaluating the integral. I need to integrate the equation for the brightness (B) over the frequency [tex]\nu[/tex] where the limits are given by the span of wavelengths in the visible part of the spectrum. The integral then just looks something like this:
    [tex]\int B[/tex]=[tex]\int \nu[/tex]3(e[tex]\nu[/tex]-1)-1 , where i excluded the constants.

    I tried integration by parts but it didn't work. I also plugged it into mathematica and got a very weird, long answer that didn't make sense. When I asked my TA about it he told me I had to solve it numerically. What does it mean to solve an integral numerically? Am I just supposed to plug in the lower limit and then subtract that from what I get when I plug in the upper limit? I am thinking of the fundamental theorem of calculus here.

  2. jcsd
  3. Jun 2, 2010 #2


    User Avatar
    Homework Helper

    This integral doesn't have a primitive in terms of elementary functions. To evaluate this integral you can use the Raleigh-Jeans approximation by looking it up in your book or by using the Taylor series of the exponent up to first order.
  4. Jun 2, 2010 #3


    User Avatar
    Science Advisor

    When you integrate a function numerically, you basically divide the area up into a bunch of narrow rectangles or trapezoids and add them all up. There are a lot of ways to do this, try reading this:


    To accomplish this, you could write a program to do it, or use a canned program. Mathematica has a function NIntegrate which will do numerical integration and, given the function and the endpoints, will just return a number.
  5. Jun 3, 2010 #4
    Thanks guys
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook