Planck's distribution law

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

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