How to Estimate Energy Density Using Planck's Law?

[johnnyies]

Homework Statement

Estimate the energy density between 499.5 and 499.6 nm emitted by a blackbody at a temperature of 2000 K. Compare to the classical value predicted by the Rayleigh-Jeans law.

Homework Equations

http://en.wikipedia.org/wiki/Planck's_law

The Attempt at a Solution

now I know how to integrate the indefinite integral of the law by setting x = $\frac{hc}{KλT}$ (K = Boltzmann constant)

T = 2000K is substituted in and we use the same substitution for λ^5 of the equation.

However I do not understand how to numerically solve this with λ = 499.5 to 499.6, would we then substitute it to x = $\frac{hc}{KλT}$ and make x the new limits of integration?

 

[Mute]

The fact that the wavelengths you are given are so close together suggests to me you just need to approximate the integral using

$$\int_{\lambda}^{\lambda+\Delta \lambda} d\lambda'~f(\lambda') \approx \Delta \lambda f(\lambda).$$