The energy per unit area per unit time per wavelength interval emitted by a blackbody at a...

The energy per unit area per unit time per wavelength interval emitted by a blackbody at a temperature T' is given by

At a specific temperature, the total power radiated per unit area of the blackbody is equal to the area under the corresponding Iλ versus A curve. Use this to derive the Stefan-Boltzmann Law. [Hint: To clean up the exponential, change variables in the integral so that

Use the fact that where the gamma function is given by  and the Riemann zeta function for n = 3 is