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Thanks for your guidance and help, learned a lot and really appreciate it. Here is a video I think you will like,

Is this the right equation to use for the answer in 24 b) ?

Last question, as for 24 b) in #10, the answer for the first intensity should be I(400nm,T) = 335289 W/m^2 https://www.wolframalpha.com/input/?i=solve%28x%2F%284.593*10%5E%286%29%29%3D0.073%2Cx%29 Just trying to plug in these values as in thread #11 but don't come up with the same answer...

The integration I outlined is used for temperature? What I don't understand quite is why wavelength is used in both energy density and intensity as the factor C/4 is used to convert between these.

So this is used for the integration?

Wavelength, is it just using the value I wrote one thread above? What will it be for frequency and temperature?

Is the procedure for the numerical integration for Planck's radiation law the same for the energy density as it is for the intensity? How is the value calculated here in b) ?

I thought maybe that an integration was necessary on the energy density, but it seems that the Wien displacement law is used to find the peak curve and then you use Stefan Boltzmann law to integrate between wavelengths within that peak. Stefan law is the Planck radiation formula multiplied by...

Here is some more useful information: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/Planckapp.html#c1 When looking at Stefan-Boltzmann law, and how the procedure is done there, is this the equation to use if I want to find the integral between 500K and 5500K...

So I also have to multiply the constant outside the integral with 2.40? What value will I use for T in the same equation on the left side if I integrate between 500K and 5500K ?

By C you mean: 8 *pi * k / (hc)^3 ?

Want to integrate the total energy density over all photon energies between two temperature values from 500K to 5800K, but not sure how to proceed. Here is some examples to help:

Really appreciate the help, now the numbers are equivalent.

I need to find the anti-derivate for the speed distribution, and all the probabilities needs to add up to one. In this example for the definite integral for kinetic energy, the answer is at the bottom of the page. https://www.wolframalpha.com/input/?i=d/du(erf(sqrt(u))-2/(sqrt(pi))*sqrt(u)*e^(-u))