Use the definite integral
\int_{0}^{∞}{\frac{x^{3}}{e^{x}-1} dx} =\frac{\pi ^{4}}{15} (14.4-7)
to derive the Stefan–Boltzmann law, Eq. (14.4-1):
(total radiant emittance)=σT^{4} (14.4-1a)
σ=5.67051 × 10^{−8} Jm^{−2} s^{−1} K^{−4}=5.67051 × 10^{−8}Wm^{−2} K^{−4} (14.4-1b)
Calculate the theoretical value of the Stefan–Boltzmann constant.