Planck’s radiation law — UPSC Physics Optional CSE 2006 Paper I

Using Planck's radiation formula u(\nu) d\nu = \frac{8 \pi h}{c^3} \frac{\nu^3 d\nu}{e^{h\nu/kT} - 1} where the symbols have their usual meaning, find the wavelength of the region where energy density is the greatest. Also calculate the total energy density over all the frequencies