Roy Vincent L. Canseco, MSEE Jan 2014
Plank’s law for Black-Body radiation takes the form
Plotting the integrand
The plot suggests that approximating the integral from 0 to infinity can be done by numerically integrating from 0 to 15.
We use the Maple implementation of the Quadrature rule with the following parameters: composite, non-adaptive and Simpson-based. We integrate from 0 to 15 and again from 0 to 20 in order to compare if there is any significant improvement from the truncating the integration at a further interval. The above plot suggests that there shouldn’t be any significant change in value.
There is less than 1% change in value, suggesting a good enough balance between efficiency and accuracy.