(adsbygoogle = window.adsbygoogle || []).push({}); 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]^{3}c^{-2}(e^{h[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.

Thanks

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# Homework Help: Black Body Radiation (Awkward integral)

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